# 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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### Which non-homogeneous scalar manifolds are possible in supergravity?

The scalar fields in various supergravity theories are restricted (by supersymmetry) to span the target (scalar) manifolds of a certain class (e.g. Hodge-Kahler, quaternion-Kahler etc.), depending on ...
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### Hypersurface Orthogonality of Conformal Killing field on Conformal Killing Horizon

Suppose we have a spacetime manifold $(\mathcal{M},g)$ admitting a conformal Killing Horizon $\mathcal{H}_c$ generated by a conformal Killing field $\chi^a$ (which is null only on the conformal ...
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### Why to introduce spinor fields we need this map in the definition of a spin structure?

Let me start with what I currently understand. Let ${\rm SO}(1,3)$ be the proper ortochronous Lorentz group. Its universal cover is ${\rm SL}(2,\mathbb{C})$. The representations of its universal cover ...
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### Degree of a multilinear product in string field theory

I am going through the paper $L_{\infty}\textit{ Algebras and Field Theory, O. Hohm and B. Zwiebach (2017) }$ (https://arxiv.org/abs/1701.08824) and I cannot for the life of me figure out how and why ...
51 views

### Is it enough to give a time-orientation to define a spin structure?

Maybe I got it wrong and my question doesn't make sense, excuse me if that's the case. For a smooth Lorentz 4-manifold $(M, g)$ with signature $(- + + +)$ is it enough to give a time-orientation to ...
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### What is the domain of momentum operator on $\mathbb{R}$?

Observables in QM are postulated to be self-adjoint operators. Those have to obey $\hat A \vphantom{A}^+ \! = \hat A$, including the equality of their domains. If we work on a finite interval $(a, b)$,...
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### Partition function $\mathrm{tr} e^{-\beta H}$ for non-trace-class operator

For Hamiltonian $H$, the partition function is defined as $$Z=\mathrm{tr} e^{-\beta H}.$$ However, consider a free particle $H = -\Delta$ in $\mathbb R^1$. In this case, the operator $e^{-\beta H}$ is ...
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### How are vector quantities in three dimensions (velocity, electric field, etc.) modeled in mathematical physics?

In introductory courses, vectors are defined as objects with direction and magnitude. I guess everyone has arrows in mind when talking about vectors and that's probably the most intuitive description, ...
3k views

### Do all Noether theorems have a common mathematical structure?

I know that there are Noether theorems in classical mechanics, electrodynamics, quantum mechanics and even quantum field theory and since this are theories with different underlying formalisms, if was ...
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### Does microcausality plus the time-slice property imply local primitive causality?

In quantum field theory, observables are associated with regions of spacetime. One of the basic principles of relativistic quantum field theory is microcausality, which says that observables ...
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### Axiomatic Quantum Theory

Is there any practical advantage/disadvantage between using the axioms for the Hilbert Space formulation as opposed to the C* Algebra formulation of Quantum Theory? If not, then is it possible to ...
420 views

### Spectral decomposition vs Taylor Expansion

This question and the comments and answers it received encouraged me to ask this question, although I know that there will be some people who think that this belongs in the math forum. But I think ...
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### Is there a more theoretical approach to studying physics? [closed]

I have read some physics papers in theoretical particle physics and all of them were based on computation, they had some mile long equations and the result was always the proof of some formula. I am ...
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### There can be degeneracy in 1D energy eigenfunctions even if one of them and its derivative does to zero as $x\to\infty$?

In 1D, the energy eigenvalue equation for an energy value $E$ $$-\frac{\hbar^2}{2m}\psi''(x) + V(x)\psi(x) = E\psi(x)$$ can have at most two linearly independent solutions, $\psi_1$ and $\psi_2$, ...
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### References on mathematical stacks for a string theory student

This question was posted on mathoverflow (here) without too much success. I'm hoping to read the famous Kapustin-Witten Paper "Electric-magnetic duality and the geometric Langlands program" ...
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### Number of bras and kets

My quantum mechanics teacher told us during the class that there were many more "bra" than "kets", but I confess that I don't quite understand this. Indeed, in quantum mechanics, ...
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### Orthogonality of two randomly chosen velocity vectors in the kinetic theory of gas and the relative velocity

I was looking for the average value of the relative velocity of ideal gas molecules in the kinetic theory. The following is from this article. The vector notation is not mathematically rigorous, just ...
56 views

### Dirac delta equalities in physics

Earlier I asked this question on the Math Exchange but I'm looking for a physics point of view. How do you interpret an equation like $$x^n \delta(x) = 0, \qquad n\in \mathbb{N},$$ around $x=0$? Why ...
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### Confusion about the dimension of a Hilbert Space in Quantum Mechanics [duplicate]

In Quantum Mechanics, the quantum state of the physical system lives in an infinite-dimensional Hilbert space and can be written in terms of two different bases, the position basis (uncountably ...
51 views

### Convergence of $c^* Ac$ in second quantization

Let $A$ denote a bounded operator on a complex separable Hilbert space $\mathscr{H}$. Let $\mathscr{F} = \bigoplus \mathscr{F}_N$ be the Fock space generated by $\mathscr{H}$ where $\mathscr{F}_N$ is ...
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### What equation should I use if I am estimating the distance of a rocket's landing point to the point it was launched from?

I am trying to figure out how to estimate how far (in meters) that a solid fuel model rocket will land from its launching point. To do this, I have figured out I will need to estimate the maximum ...