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# Questions tagged [mathematical-physics]

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 mathematical methods to problems in physics. Examples include partial differential equations (PDEs), variational calculus, functional analysis, and potential theory.

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### Mathematical background for Quantum Mechanics [duplicate]

What are some good sources to learn the mathematical background of Quantum Mechanics? I am talking functional analysis, operator theory etc etc...
5k views

### “Velvet way” to Grassmann numbers

In my opinion, the Grassmann number "apparatus" is one of the least intuitive things in modern physics. I remember that it took a lot of effort when I was studying this. The problem was not in the ...
1k views

### Why is the Gupta-Bleuler gauge unfashionable?

In the early days of quantum electrodynamics, the most popular gauge chosen was the Gupta-Bleuler gauge stating that for physical states, $$\langle \chi | \partial^\mu A_\mu | \psi \rangle = 0.$$ ...
245 views

### Singularities in Bianchi models in general relativity ( physical science)

what are the conditions to check point type singularity in a bianchi type model ? bianchi type model are of Type I,II,III,IX,IV or u can say we use different Bianchi type models having some specific ...
2k views

### Why is there a deep mysterious relation between string theory and number theory, elliptic curves, $E_8$ and the Monster group?

Why is there a deep mysterious relation between string theory and number theory (Langlands program), elliptic curves, modular functions, the exceptional group $E_8$, and the Monster group as in ...
307 views

### A question about a vibrating membrane

The usual way to model a vibrating membrane is by using the wave equation. Is it possible to do that from "within"? Probably the answer is yes, but where can I see it done explicitly. What I mean is ...
236 views

### Does the positive mass conjecture indicate a necessity of interactions in our universe?

The positive mass conjecture was proved by Schoen and Yau and later reproved by Witten. Total mass in a gravitating system must be positive except in the case of flat Minkowski space, where energy is ...
3k views

### What's the point of having an einbein in your action?

One often comes across actions written with an extra auxiliary field, with respect to which if you vary the action, you get the equation of motion of the auxiliary field, which when plugged into the ...
4k views

### What does John Conway and Simon Kochen's “Free Will” Theorem mean?

The way it is sometimes stated is that if we have a certain amount of "free will", then, subject to certain assumptions, so must some elementary particles."(Wikipedia) That is confusing to me, ...
2k views

### Non-linear Schrödinger equation

I have read about the existence of a non-linear scrhödinger equation. What is its utility and application? And how can it be derived? Is it in a relativistic or non-relativistic context?
5k views

### Formalizing Quantum Field Theory [duplicate]

I'm wondering about current efforts to provide mathematical foundations and more solid definition for quantum field theories. I am aware of such efforts in the context of the simpler topological or ...
219 views

### Question on particles

Is there any theory in which every particle can be further subdivided into any number of particles and the total number of particles any where in the space time are infinity in theory and only due to ...
451 views

### Variational method applied to brownian motion

It's possible apply the variational method to the brownian motion ? I mean, one of requisites on $y(t)$ is that it must be continuous and $\partial_t{y(t)}$ too, and in this case, $\partial_t{y(t)}$ ...
340 views

### Renormalization and Infinites

Measuring a qubit and ending up with a bit feels a little like tossing out infinities in renormalization. Does neglecting the part of the wave function with a vanishing Hilbert space norm amount to ...
1k views

### The derivation of fractional equations

Recently I saw some physical problems that can be modeled by equations with fractional derivatives, and I had some doubts: is it possible to write an action that results in an equation with fractional ...
2k views

### What is a maximal analytic extension?

Can someone explain (as rigorously as possible) what is involved in analytically continuing, say, the Schwarzschild solution to the Kruskal manifold? I understand the two metrics separately but I'm ...
6k views

### Haag's theorem and practical QFT computations

There exists this famous Haag's theorem which basically states that the interaction picture in QFT cannot exist. Yet, everyone uses it to calculate almost everything in QFT and it works beautifully. ...
2k views

### Is causality a formalised concept in physics?

I have never seen a “causality operator” in physics. When people invoke the informal concept of causality aren’t they really talking about consistency (perhaps in a temporal context)? For example, if ...
699 views

### How do we resolve operator ordering ambiguities when quantizing generic nonlinear second-class constraints?

Dirac came up with a general theory of constraints, including second-class constraints. To quantize such systems, he first computed the Dirac bracket classically, and only then "promoted" the ...
474 views

### What is the quantum / Berry-Pancharatnam phase for a spin-j state with z-component m?

Quantum phase arises when a spin-j state is sent through a sequence of transitions that return it to its original position. For example with spin-1/2, a state picks up a complex phase of $\pi/4$ when ...
3k views

### What is the relation between renormalization in physics and divergent series in mathematics?

The theory of Divergent Series was developed by Hardy and other mathematicians in the first half of the past century, giving rigorous methods of summation to get unique and consistent results from ...
575 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?
375 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 (e....
889 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 ...
8k 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 ...
471 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 ...
363 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 ...
6k 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 ...
4k 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 ...
5k 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 ...
3k 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 Ludwig: ...
10k 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 ...
11k 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 ...
10k views

### Classical mechanics without coordinates book

I am a graduate student in mathematics who would like to learn some classical mechanics. However, there is one caveat: I am not interested in the standard coordinate approach. I can't help but think ...
1k 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 ...
5k 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 ...
1k 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. ...
10k 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 ...
2k views

### Books for linear operator and spectral theory

I need some books to learn the basis of linear operator theory and the spectral theory with, if it's possible, physics application to quantum mechanics. Can somebody help me?
448 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 ...
11k views

### Number theory in Physics [closed]

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 ...
43k 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: ...
2k views

### How do physicists use solutions to the Yang-Baxter Equation?

As a mathematician working the area of representation of Quantum groups, I am constantly thinking about solutions of the Yang-Baxter equation. In particular, trigonometric solutions. Often research ...
Noether's theorem states that, for every continuous symmetry of an action, there exists a conserved quantity, e.g. energy conservation for time invariance, charge conservation for $U(1)$. Is there any ...