DO NOT USE THIS TAG just because your question involves math! If your question is on simplification of a mathematical expression, please ask it at math.stackexchange.com Mathematical physics is the mathematically rigorous study of the foundations of physics, and the application of advanced ...

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5answers
471 views

Black Hole Singularities

If two black holes collide and then evaporate, do they leave behind two naked sigularities ore? If there are two, can we know how they interact?
10
votes
2answers
310 views

What is known about some massive Gaussian models on a lattice?

Recently I started to play with some massive Gaussian models on a lattice. Motivation being that I work on massless models and want to understand the massive case because it seems easier to handle ...
4
votes
1answer
581 views

Properties of graph of subatomic particle interactions

Say there was some situation where you have a lot of subatomic particles interacting with each other and decided to draw (say, by joining Feynmann diagrams) those interactions- so that you got some ...
14
votes
8answers
3k views

Crash course on algebraic geometry with view to applications in physics

Could you please recommend any good texts on algebraic geometry (just over the complex numbers rather than arbitrary fields) and on complex geometry including Kahler manifolds that could serve as an ...
20
votes
4answers
412 views

Paradox?: What is the form of radiation experienced by a harmonically accelerated observer?

Theory predicts that uniform acceleration leads to experiencing thermal radiation (so called Fulling Davies Unruh radiation), associated with the appearance of an event horizon. For non uniform but ...
1
vote
1answer
338 views

Cheetah prosthesis efficiency

I want to compare the much-talked about Cheeta running prosthesis to a the normal running process in terms of force and energy, but I don't know where to start. How would you start the comparison? A ...
12
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3answers
2k views

Ring theory in physics

Surely group theory is a very handy tool in the problems dealing with symmetry. But is there any application for ring theory in physics? If not, what's this that makes rings not applicable in physics ...
21
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3answers
2k views

Why are von Neumann Algebras important in quantum physics?

At the moment I am studying operator algebras from a mathematical point of view. Up to now I have read and heard of many remarks and side notes that von Neumann algebras ($W^*$ algebras) are important ...
10
votes
4answers
2k views

Where is the Atiyah-Singer index theorem used in physics?

I'm trying to get motivated in learning the Atiyah-Singer index theorem. In most places I read about it, e.g. wikipedia, it is mentioned that the theorem is important in theoretical physics. So my ...
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votes
2answers
1k views

Jauch, Piron, Ludwig -> QFT? [duplicate]

Possible Duplicate: What is a complete book for quantum field theory? At the moment I am studying Piron: Foundations of Quantum Physics, Jauch: Foundations of Quantum Mechanics, and ...
16
votes
4answers
3k views

A pedestrian explanation of conformal blocks

I would be very happy if someone could take a stab at conveying what conformal blocks are and how they are used in conformal field theory (CFT). I'm finally getting the glimmerings of understanding ...
20
votes
10answers
4k views

Applications of Algebraic Topology to physics

I have always wondered about applications of Algebraic Topology to Physics, seeing as am I studying algebraic topology and physics is cool and pretty. My initial thoughts would be that since most ...
25
votes
8answers
3k views

Classical mechanics without coordinates book

I am a math grad student who would like to learn some classical mechanics. The caveat is I am not to interested in the standard coordinate approach. I can't help but think of the fields that arise in ...
5
votes
2answers
871 views

Separation of variables, eigenfunctions of the Dirac operator

Disclaimer: I am not a physicist; I am a geometer (and a student!) trying to learn some physics. Please be gentle. Thanks! When solving the Schrödinger equation for a particle in a spherical ...
2
votes
1answer
2k views

Spherical wave as sum of plane waves

How can we do this computation? $\iiint_{R^3} \frac{e^{ik'r}}{r} e^{ik_1x+k_2y+k_3z}dx dy dz$ where $r=\sqrt{x^2+y^2+z^2}$ ? I think we must use distributions... Physically, it's equivalent to ...
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votes
5answers
1k views

Hubble's law and conservation of energy

If all distances are constantly increasing, as Hubble's law say, then lots of potential energies of form ~$\frac{1}{r}$ changes, so how is the total energy of the Universe conserved with Hubble's ...
23
votes
6answers
3k views

Why does calculus of variations work?

How does it make sense to vary the position and the velocity independently? Edit: Velocity is the derivative of position, so how can you treat them as independent variables? Doesn't every physics ...
13
votes
2answers
706 views

Is the G2 Lie algebra useful for anything?

Seems like all the simpler Lie algebras have a use in one or another branch of theoretical physics. Even the exceptional E8 comes up in string theory. But G2? I've always wondered about that one. ...
25
votes
13answers
3k views

Suggested reading for renormalization (not only in QFT)

What papers/books/reviews can you suggest to learn what Renormalization "really" is? Standard QFT textbooks are usually computation-heavy and provide little physical insight in this regard - after my ...
4
votes
5answers
578 views

If the size of universe doubled

My question is silly formulated, but I want to know if there is some sensible physical question buried in it: Suppose an exact copy of our universe is made, but where spatial distances and sizes are ...
5
votes
3answers
303 views

What is necessary for a causal set to be manifold-like?

A causal set is a poset which is reflexive, antisymmetric, transitive and locally finite. As a motivation, there is a programme to model spacetime as fundamentally discrete, with causal sets ...
51
votes
14answers
5k views

Number theory in Physics

As a Graduate Mathematics student, my interest lies in Number theory. I am curious to know if Number theory has any connections or applications to physics. I have never even heard of any applications ...
44
votes
13answers
9k views

Best books for mathematical background?

What are the best textbooks to read for the mathematical background you need for modern physics, such as, string theory? Some subjects off the top of my head that probably need covering: ...
6
votes
3answers
584 views

Impressions of Topological field theories in mathematics

There have been recent results in mathematics regarding Conformal field theories and topological field theories. I am curious about the reaction to such results in the physics community. So I guess a ...
33
votes
8answers
3k views

Is there something similar to Noether's theorem for discrete symmetries?

Noether's theorem states that, for every continuous symmetry of a system, there exists a conserved quantity, e.g. energy conservation for time invariance, charge conservation for $U(1)$. Is there any ...