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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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### What does mathematical consistency in QFT mean?

My question is more naive than Is QFT mathematically self-consistent? Just when people talk about the mathematical consistency of QFT, what does consistency mean? Do people want to fit QFT into ZFC? ...
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### Existence of informationally complete POVM on infinite dimensional Hilbert space

Do there exist informationally complete POVM (in this sense) on infinite dimensional separable Hilbert spaces? It is known that these exist in finite dimensions (I believe they were used in the proof ...
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### Complex, Holomorphic connection, and Symplectic — a not-so-Kähler manifold?

While studying mathematical physics, I wondered whether if there is a mathematical theory for a manifold that has a complex structure [almost complex structure $J^\mu{}_\nu$ with vanishing Nijenhuis ...
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### Path Integral for Fokker-Planck equation

As per Wio, the special case of the Fokker-Planck equation (in SDE form) \begin{equation*} dX = f(x)dt + \sqrt{2D} dW_t \end{equation*} has the path integral representation in the Ito scheme as \...
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### Wightman QFTs corresponding to Minimal Models

Per suggestion, I am cross-posting the following question from MathOverflow (original). At MO, Abdesselam referenced the work . Glancing through it, is not immediately obvious to me how far the ...
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### Mathematically rigorous QFT text

There are multiple questions on here about QFT textbook recommendations, but I am looking for mathematically precise texts on QFT. Recommendations of introductory and advanced texts are welcome, but ...
1 vote
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### What is the name of this construction of quantum things?

Let $E$ be a set, and let $\mathcal{F}$ be a set of maps $E \rightarrow \mathbb{R}$ that "carries all the information on $E$", that is, the map $x \in E \mapsto (f(x))_{f \in \mathcal{F}}$ ...
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### Can we determine when the lowest-energy state cannot be annihilated by any local operator, just by inspection of the Hamiltonian?

Relativistic quantum field theory (QFT) has the property that the lowest-energy state cannot be annihilated by any operator that is localized in a finite region of space (references 1,2,3). In other ...
### Is the momentum operator self-adjoint on any bounded interval on $\mathbb{R}$?
I know that the momentum operator $p$ defined on the Schwarz function $S(\mathbb{R})$ is essentially self-adjoint. However, what if I were to restrict $p$ to $C_c^\infty (0,1)\subseteq L^2(0,1)$. In ...
Let there be a a quantum field operator $\hat\phi(t,\vec{x})$ which, because it acts (pointwise) on a separable Hilbert space, I expect I can write as \hat\phi(t,\vec{x}) = \sum_n\sum_m\phi^n_m(t,\...