Geometry of String Theory Solitons

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by
Magnus Holm
Institute of Theoretical Physics
Chalmers University of Technology and Göteborg University – Göteborg 1999

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Abstract
In recent years there has been a dramatic progress in the understanding of the non-perturbative structure of various physical theories.
In particular string theory has been vastly developed during these years, where a lot of duality conjectures between the different string theories have arisen.
The introductory text of this thesis is an attempt to describe this development in short and to make a brief overview of the subject.
Special focus is put on solitonic solutions in various field theories, which is the corner stone for these duality conjectures.
The introduction of supersymmetry is also essential for the understanding of duality by its natural way of handling BPS-states through the algebra.
In string theory, which is not only a supersymmetric theory but also includes gravity, these studies are put together through the discovery of various p-brane solutions to the background field equations.
The geometrical structure of these solutions is studied in some of the papers in this thesis.
In a generalization to the treatment of p-branes as solutions which break the local vacuum symmetry, the theory of almost product structures (APS-theory) has arisen as the natural candidate to the study of the intricate geometry of these solutions.
The last two papers deal with this ansatz where it is also seen that APS-theory is the most natural way of treating all kinds of splitting of manifolds including fibrations, Yang-Mills theoryand Kaluza-Klein theory.
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391 comments to Geometry of String Theory Solitons

  • Hello Dr Rossi:

    In a few weeks, you will be inundated by commercial requests for ordinary engineers to try to sell into your market.

    Will you be giving those of us who have supported LENR for many years any kind of advantage?

    In particular, right now I am marketing Industrial Custom Memory solutions, in DDR and in Flash. I would hope that you’d consider us in your designs.

    best regards

    Kevin O’Malley
    Field Application Engineer
    Innodisk Corporation http://www.innodisk.com
    humans will know this phone number: 408 four six -oh- 57 -0h- 7

  • Andrea Rossi

    Alutam:
    This is a very interesting question, and, as I can remember, it has not been forwarded before.
    I think that 6 month is a prudential shelf life term, because we already happened to store for 6 months a charged E-Cat before putting it in operation.
    Thank you, good point.
    Warm Regards,
    A.R.

  • alutam

    Andrea,
    I’m not sure if this has been asked before. Does an E-Cat have a shelf life?
    After it is made must it be put to use soon or can it be stored in a warehouse for months or years until it is needed and still perform its function?
    Best Regards.

  • Andrea Rossi

    Andreas Moraitis:
    The physics of the so called discrete breathers are very interesting. Good paper, thank you for citing it to our Readers.
    Warm Regards,
    A.R.

  • Andreas Moraitis

    Dear Andrea Rossi,

    Perhaps the following paper from Kharkov Institute (Ukraine) could be of interest:

    http://arxiv.org/abs/1406.3941

    Best regards,
    Andreas Moraitis

  • Marc F

    Dear Andrea:
    Just came across this article today.
    Think about the millions of lives that could be saved by incorporating the E-Cat into this device:
    http://www.popsci.com/article/science/pure-genius-how-dean-kamens-invention-could-bring-clean-water-millions

    Marc

  • Andrea Rossi

    Manuel Cilia:
    Just contact
    info@leonardocorp1996.com
    Warm regards
    A.R.

  • Dear Mr Rossi,
    Have you had any changes to the method of purchasing Ecat’s? Will it be through the licenced dealers or by other methods? I have had many inquiries about purchasing Ecats from my clients and I do not know why they think I can get one, maybe because I have been talking about you and the Ecat for so long.
    Thank you for all your blood sweat and tears.

  • Andrea Rossi

    Ville Kanninen:
    It is impossible to answer to your question, or, at least, I am not able to. I do not know what the competition will do. One thing I am sure of is that from competition will rise more convenience for the market. Remember: ” In mercatu veritas “. I know that giants are already working to compete with us: Shell, Mitsubishi, MIT, Volvo, ABB, NASA…and I am strongly honoured to have inspired, in some way, their work; to be clear: should I have not broken the ice in three years of public work, since January 2011, none of these Entities would have taken seriously LENR in the measure they are taking them now. Is it not true? At the cost of tremendous fights that also involved personal issues that have nothing to do with my work, but still have consumed time and energies. Anything has been tried to kill our work, without substantial effects, though ( thanks to God). Our Team is stronger than ever.
    Warm Regards,
    A.R.

  • Andrea Rossi

    Mike Phalen:
    1- Wrong and I cannot disclose our patents strategy, that is dealt with by a team of attorneys expert of the matter
    2- Intellectual property is a complex issue, not as simple as you represent. Licensing is a complicate issue as well and I cannot give more information about our licensing strategy either at the moment
    3- These are issues whose development is integrated in a complex and wider decisional system
    4- Indipendently from the points 2 & 3, that would be anyway useful, provided it is also integrated in our decisional system
    Warm Regards,
    A.R.

  • Dear Andrea Rossi,

    I know that you have commented on the Ecat patent situation in the past.

    1. How do you currently feel about being unable to obtain a patent for the Ecat?

    2. If a patent was granted do you feel it would speed up the process of licensing the Ecat technology to 3rd parties?

    3. Would it quicken the spread of the Ecat around the world?

    4. If the answer to 2 & 3 is yes. After the report is released would it be helpful if someone were to work to raise the awareness of the public and government that this situation exists?

  • Dear Andrea Rossi,

    If we suppose that both your commercial plants and the scientific test results will be success – as we all hope here – then many things will follow. This will then certainly happen: governments in USA, EU, China, Japan, South-Korea etc. will start to pour billions and billions of dollars to LENR research.

    Do you think that the coming research around the world following your invention will reveal several different new practically useful LENR processes?

    Or do you think that what you found is more probably the only practically useful LENR process just maybe having several useful variations?

    Kind regards

    Ville Kanninen

  • Andrea Rossi

    H-B Branzell:
    Correct, or, to use Giuliano Bettini’s mode, it’s TPR2 ( I understood, anyway, what’s behind your message and I thank you).
    Warm Regards,
    A.R.

  • H-B Branzell

    Dear Andrea Rossi,

    The Party from which we are expecting a new report is not the Third in a sequence of Independent Parties.

    It is the second Independent Third Party.

    Kind regards, H-G Branzell

  • DTravchenko

    Thank you for your answer . Please remind that in our Country your E-Cat and your person are strongly appreciated.
    From Russia with love,
    D.T.

  • Curiosone

    Dear Andrea Rossi:
    Thank you for your lecture about the 4 foundamental forces and the 4 foundamental magnitudes: as always you have been able to explain Physics to not skilled persons.
    Thank you to dedicate your time to us,
    W.G.

  • Andrea Rossi

    Giuliano Bettini:
    After the 2013 test, the Third Independent Party has made all the measurements of the 2014 test considering all the experience from the work made in 2013.
    We have to wait patiently the results, positive or negative as they might be. I cannot intercede for anything.
    Warm regards
    A.R.

  • Giuliano Bettini

    Dear Andrea Rossi.
    About the PCE 830 in the TPR1.
    Regarding the measurement of P input, there is a eternal and annoying debate.
    Because the involved engineers and technicians are very reputable from both sides of the debate, can you please intercede with the Profs, so that they clarify?
    Thanks,
    Giuliano Bettini.

  • Andrea Rossi

    Curiosone:
    I try to answer to your quest as simply as possible.
    The 4 foundamental forces are a totally different thing from the 4 foundamental magnitudes.
    The 4 foundamental forces are:
    Strong: strong force is mediated by gluons, which hold together quarks to make protons and neutrons; gluons and quarks are confined inside protons and neutrons by “colours”.
    Electromagnetic: electromagnetic force is mediated by photons, as we have seen in a former comment of mine
    Weak: weak forces are mediated by the gauge bosons W+, W- and Z, which are responsible for the decay of neutron into protons ( easier, since the mass of n is more than the mass of p, so energy is conserved by the emission of anti-neutrinos) and the decay of protons in neutrons ( more difficult, for the same reason: it is possible only in a more complex system of interactions between more particles and the formation of virtual particles that eventually decay into neutrons). W+, W- and Z are the sole elementary particles that change the nature of the particles they interact with.
    Gravitational: gravitational forces are mediated by gravitons: if the Moon orbits around the Earth, this happens because Earth and Moon exchange gravitons.

    The 4 foundamental magnitudes are:
    Rest Mass: m = E/c^2 x square root of (1- v^2/c^2)
    Electric Charge: -1, 0, +1 respectively for electrons, neutrons and neutrinos, protons; -1/3 for down quarks, +2/3 for up quarks
    Spin: spin is the intrinsic angular momentum and its quantum is h/ 4pi, where h is the Plank constant and pi = 3.14; spin is positive if counterclockwise, negative if clockwise
    Magnetic momentum: it can be -1, 0 or +1 and its quantum is 9.29 x 10^-24 J/T
    Energy, electric charge, spin and magnetic momentum are conserved: after any interaction, the sum of them must be the same as before the interaction.
    Hope to have been useful,
    Warm Regards,
    A.R.

  • Andrea Rossi

    D. Travchenko:
    1- About Enerkem: it definitely has utilized my patent of 1978 ( expired in 1998), and I am delighted to see that my work of 35 years ago is generating good results.
    2- About the other issue: please, everybody must understand that a man must be considered innocent, until an irrevocable verdict is issued; the presumption of innocence is a right of everybody. The Guardia di Finanza is a glorious military institution, with about 100 000 military heroes that every day fight honestly and for a modest wage, risking their life to defend Italian economy and the respect of the Law. Any other consideration is useless at this time.
    Warm Regards,
    A.R.

  • Andrea Rossi

    D. Travchenko:
    Good question. We will put our plants wherever they will be wanted, along the market waves vibrations. Russia is a great Country, with a tremendous potential and we are looking for Russia with extreme interest.
    Warm Regards,
    A.R.

  • Andrea Rossi

    Curiosone:
    Sweden: we are making up in Sweden a very strong team of young, aggressive and very well prepared physicists with strong enterpreneurial bases. Sweden is also a logic place for the development of the E-Cat , due to the weather, and the system of distributed heating that is fit for our technology. Obviously we are also looking with deep respect all the other Countries of the world, but you asked me which place will be first: I think Sweden. Also because I want to make the Vasaloppett before getting too old ( he,he,he…).
    Warm Regards,
    A.R.

  • DTravchenko

    Dear Andrea Rossi:
    Canada, Québec- Edmonton: Enerkem has started up a plant that makes biofuel from organic wastes, with a technolgy derived from your patent of 1978. Are you proud of it? In the meantime, the General of the Guardia di Finanza of Italy ( Google ” Generale Emilio Spaziante arrestato”) who directed from 1989 the fight against you stopping your plants has been arrested for corruption: do you feel vindicated from these two events ?
    From Russia with love,
    D.T.

  • DTravchenko

    Dear Andrea Rossi:
    Do you think that your plants will be installed also in Russia? Do you understand that you have here very high level friends that are following with great attention your work, since 2011, when important scientists of our science Academy have been sent to attend your experiment?
    From Russia with love,
    D.T.

  • Curiosone

    Dear Readers of the JoNP:
    A theoretical question, from a non physicist: are the 4 foundamental forces the same things as the 4 foundamental magnitudes ? Can anybody explain in simple Language, without mathematics, so that a layman as I am can understand ( like Andrea Rossi made explaining what is a photon )?
    W.G.

  • Curiosone

    Dr Andrea Rossi:
    We know that the first plants of 1 MW will be made in the USA. Where do you think will be made the following ones outside the USA? Which will be the places you think will be privileged? Can you give a hint of this?
    Thank you for the time you dedicate to us,
    W.G.

  • Andrea Rossi

    Dear Readers:
    Update to your FAQ:
    1- Report: I still do not know when the report will be published, as it is not under my control.
    Remember: the results could be positive or negative.
    If I receive information about publication timeframes, I will share it at that time. Otherwise, for me, it is clearly impossible to share information I do not have.
    2- R&D: we have a robust R&D program, consistent with the expectations of the market. As the chief scientist, I focus on improving the operation of the E-Cat, ensuring quality control, testing and evaluation.
    3- Our Customers: information about our Customers, obviously, is confidential. When visits to a plant operated by a Customer of us in his factory will be ready to be allowed, due information will be given to the accepted Visitors.
    Warm Regards,
    A.R.

  • Steven N. Karels

    Jaroslaw Bem,

    What’s a factor of 10 among friends? Thanks for the analysis.

  • Jaroslaw Bem

    Steven N. Karels

    You wrote June 8th 2014 “One gram of converted mass = 2700 MWHrs of energy.” And “If an eCat is run at 10kW average output for one year, about 87 MWhrs of energy would have been produced assuming continuous operation. Therefore, about 0.03 grams of mass would have been consumed.”

    My calculation show that 1 g = 25 GWh energy:
    E = mc^2
    m = 1 g = 0.001 kg
    c = 3 E+8 m/s
    E = 0.001 kg * (3 E+8 m/s)^2 = 9 E+13 J
    To convert energy J (Joule) to GWh :
    1 GWh = 3.6 E+12 J
    Then
    E = 9 E+13 (J) / 3.6 E+12 ( J/GWh) = 25 GWh
    Then
    1 g = 25 GWh

    Follow this: 87 MWh energy produced for one year by ECAT = 0.003 g

    Best regards
    Jaroslaw Bem
    Poland

  • Steven N. Karels

    eernie1,

    I am not lightly dismissing anti-matter. But I am ignorant of such interactions and thus the possibility. I believe it would be a more difficult explanation for most Physicists to accept it as plausible. But Andrea Rossi need not explain his reaction. Others will probably do that. His is the task of demonstrating positive results through credible and totally independent means. I think he is on the right track, if the results are positive.

  • eernie1

    Steven,
    I would not dismiss Anti-matter so quickly. Positron emission from reverse Beta decay combining with external electrons to produce Gamma photons has been observed.

  • Andrea Rossi

    Steven N. Karels:
    Yes, you have understood: we have to go forward step by step, maintaining solid hold with the soil we are marching through. Otherwise the dream will be destroyed.
    Warm Regards,
    A.R.

  • Andrea Rossi

    Dr Joseph Fine, Matt Robinson:
    simply delighting.
    Warm Regards,
    A.R.

  • Andrea Rossi

    Frank Acland:
    You are right, I agree.
    Warm Regards,
    A.R.

  • Frank Acland

    Dear Andrea,

    Thank you for the useful clarification regarding the 1 MW Plant. The fact that it will be a working E-Cat providing useful energy for someone is important.

    I hope when the time comes, the customer will be able to provide data regarding energy usage, costs, savings, etc. This is very important to people considering adopting a new source of energy.

    Best wishes,

    Frank Acland

  • Steven N. Karels

    Koen,

    Elegantly written. But all I have is Einstein’s equation and the relationship of generated energy requires an appropriate mass reduction. Nuclear Physics is not my primary expertise. But what I have read and what I understand is that some form of fusion is most likely the mechanism in LENR. There are only a limited number of known fusion reactions and each reaction consumes certain elements and generates new elements or isotopes. Until before and after measurements are made on the fuel, we will be “whistling in the wind”. Anti-matter is my least probable solution. Unless we first discover Klingons, Vulcans and DiLithium crystals (LOL).

  • Joseph Fine

    Dear Andrea Rossi,

    Matt Robinson wrote a new poem about the E-Cat and the Third Party Independent Tests. Giuliano Bettini and I made some minor contributions to this effort. I didn’t want to risk making further changes to it, so here it is. It was intended to come out before the Independent Report while I wanted it to come out before Friday 13th. I apologize for any grammatical, spelling or alignment errors. Enjoy.

    Poetic regards. 😉 -JF

    _____________________________________________

    IN MERCATU VERITAS by Matt Robinson *

    Composed with contingency dependent on the positive outcome of a certain report allegedly being prepared for publication, and a slight nod to T. S. Eliot’s ‘Macavity’

    A word of caution ‘fore you read,
    this is based on supposition
    That certain tests, we hear complete,
    could bolster my position.

    I feel that we are getting near
    the day the news will break
    I’m hoping that it’s positive,
    for all our children’s sake.

    The Rossi Cat ‘s a mystery cat,
    but some have claimed they saw
    The undeniable evidence
    that truth defies the ‘Law’.

    Unmentioned in the media,
    by others ‘t is denied
    But Rossi says, in all due time,
    the people will decide.

    The news that’s been kept hidden from
    the Wall Street’s opening bell
    Is going to be released quite soon,
    Confidently, I foretell.

    But I wish that they would hurry up
    and get the data written
    So then I can prepare my home
    for my new domestic kitten.

    The day is fast approaching when
    to all ‘t will be revealed
    The book of evidence, held ‘loft,
    and publicly unsealed.

    Yet once again we’ll hear the cry,
    ‘A hoax!’-‘They all have lied!’
    But now’s the time that truth will out,
    the people will decide.

    So what if Big Financiers plot,
    and try to keep it hidden
    And Big Science and the media
    do whatever they are bidden?

    Well, if it’s mass-produced in China,
    there’ll be a thousand on each tide
    And Rossi says, in all due time,
    the people will decide.

    Health and Safety staff, and Customs men,
    will intercept and frisk her
    They’ll scrutinize the paws and ears,
    and in between each whisker.

    The ones that know, that’s you and I,
    will regard this all as fickle
    For all that they will find inside
    is a small amount of Nickel.

    There’ll be Cats in every quarter,
    from Beijing to Peru
    You’ll even find them purring
    in far off Kathmandu.

    They’ll heat our homes, desalinate,
    and go on to power our flight
    And the people will decide for sure,
    ‘t was Rossi that was right!

    And when she’s all fired up and hot,
    and the steam begins to flow
    ‘Tis then that we can stand up proud,
    and say ‘We told you so’.

    The Rossi cat will shake the world,
    all tests have been applied
    Released unto each continent,
    the market will decide.

    At the closing peal of Wall Street’s bell
    on that day of great renown
    The Bulls and Bears will pull their hair,
    their world turned upside down.

    The Cat becomes a Lion, and
    she’ll stalk the world with pride
    It won’t have taken very long
    for the people to decide.

    We’ll owe him a great indebtitude,
    his name will be revered
    Long after all detractors and
    the snakes have disappeared.

    Our children will be born into
    a future warm and bright
    The mystery? It’s history,
    the E-Cat works, alrrrrright!

    We’re telling you that times have changed,
    the future’s in our hands-
    The wheel has turned full circle,
    the past buried in the sands.

    Empires have all come and gone,
    that’s plain to one who thinks
    Tomorrow has a bright new dawn-
    all thanks to Rossi’s ‘Sphinx’.

    * (with suggestions from Giuliano Bettini and Joseph Fine)

  • Steven N. Karels

    Dear Andrea Rossi,

    Certification is but a detail. I dream of eCats and of a Mouse and a Cat and maybe a Tiger or two. I foresee a future with eCat technology everywhere. Where children think we lived in caves before the advent of eCats. How could anyone possibly live without this technology?? — will be the resounding echo throughout the future ages?

    Andrea, my friend, you live in the world of certification, making it work, designing it better, deadlines, budget issues. I fly through the dream world of possibilities, of opportunities, of delight. Mine is a sweeter path then yours, until you make it all work. Then we shall all stand in awe in your presence (LOL). But for right now, today, make it work!

  • Andrea Rossi

    Alutam:
    At the moment it is not feasible.
    Warm regards,
    A.R.

  • alutam

    Andrea,
    You have previously mentioned smaller e-cat testing. Would a small device the size of a spark plug, hollow in the center and fitted with an injector for water to flash to steam, be a suitable replacement for a spark plug in an internal combustion engine? Just fill the tank with water instead of gas?
    Regards.

  • Koen Vandewalle

    Steven,
    Indeed, E-cat will leave some ash:
    that of burnt critics.

    As for good tradition, their masters will dump that ash somewhere.
    That’s a shame. Some were good looking and eloquent writers.

    About the nuclear ash: the more uncomplete the theories that are written, spread and teached, the more difficult it becomes to link the true parts of them and find truth.
    There seems to exist numerous kinds of Higgs-Bosons. If antimatter can be created in colliders, then this may indicate that matter or antimatter are self-creating. Maybe just as waves, driven from the Higgs Bosons. When matter and antimatter are fused, maybe just the Higgs Bosons are merged, which afterward creates new matter or anti-matter. The resulting structure (proton, neutron, electron or their anti-equivalent) and released energy may depend on the collision parameters, and therefore be as unpredictable as the weather. One could wonder if this also happens in stars. Do we have instruments that can observe the non-creation of anti-matter, or the merging or non-merging of Higgs Bosons in stars ? So how sure can we then be of theories ?
    I really don’t know. Just reading and trying to understand as much as possible, just like you and many others here on JoNP. About what happens in E-cat: Andrea Rossi’s silence is rock solid. Just keep drilling, my friend. The blog of JoNP is thousands of pages long now. It is a goldmine. At least we have that.

    Kind regards,
    Koen

  • Andrea Rossi

    Steven N.Karels:
    This kind of utilization is not certified for.
    Warm Regards,
    A.R.

  • Steven N. Karels

    Using eCat Technology for a Campfire

    Could an eCat reactor be used to replace wood for a typical campground fire?

    Assumptions:
    5 lbs of seasoned wood (20% moisture), lasts 6 hours.
    20MBTUs/cord, 85 lbs/cord

    Energy produced by campfire wood burning = 5 lbs * 20MBTUs/cord * 1 cord/85 lbs = 1.17 MBTUs = 1.234 * 10+9 Joules

    Average Power = 1.234 * 10+9 Joules / 21,600 sec = 5.7 * 10+4 W = 57 kW

    About 5 or 6 eCat 10kW reactors could produce the heat of a typical campfire.

  • Andrea Rossi

    Frank Acland:
    It is not a plant for display. It is a plant that will be installed in the factory of a Customer to work and make profit from its work. It is not a test, as made so far. I cannot give more specific information now, I am not allowed to.
    Warm Regards,
    A.R.

  • Andrea Rossi

    LMV:
    Every action produces a reaction equal and contrary, as you know: I suggest anybody not to kick anything ( he,he,he). Allowed visitors will have all the possible and due information, but it is not a theater, it is the factory of a Customer.
    Warm Regards,
    A.R.

  • LMV

    Hi Andrea
    This is as important as the TIP report
    Can the visitors “kick the wheels ” and check a few things out?

  • Frank Acland

    Dear Andrea,

    Are you making a brand new 1 MW plant in North Carolina for display — or refurbishing the one you shipped from Italy?

    Many thanks,

    Frank Acland

  • Andrea Rossi

    Eernie 1:
    …which have been made in North Carolina!
    Warm Regadrds
    A.R.

  • eernie1

    Dear Andrea,
    Displaying the 1MW plant will be like the Wright brothers first flights.

  • Andrea Rossi

    Eernie1, Steven N. Karels:
    Obviously we are talking of an industrial 1 MW plant in continuous operation in the factory of a Customer.
    Warm Regards,
    A.R.

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