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Results tagged with mathematical-physics
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user 246747
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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Functional Integral in Statistical Mechanics
In this work, the author state that many problems in statistical mechanics center on the analysis of functional integrals of the form:
\begin{equation}
Z(\varphi') = \int d\mu(\varphi) e^{-V(\varphi+\ …
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1
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1
answer
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Formulating the variational principle in grand canonical ensemble
After a very nice discussion in my previous question, I decided to move on and try to formulate the variational principle for the grand canonical ensemble. I tried following the references cited in th …
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Formulating the variational principle in grand canonical ensemble
Attempted Proof: Suppose we have a family $\{f_{N}\}_{N\in \mathbb{N}}$ of functions $f_{N}: \Omega_{N} \to \mathbb{R}$. It induces a function $f: \Omega \to \mathbb{R}$ by setting
$$f(x,N) := f_{N}(x …
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Can Feynman-Kac formula relate to partition function in a rigorous way?
Feynman-Kac formula reads:
$$\psi(x,\beta) = \int e^{\int V({\bf{x}}(\tau))d\tau}\psi_{0}({\bf{x}}(\beta))d\mu_{x}({\bf{x}}). \tag{1}\label{1}$$
This is a rigorous formula, defined by means of a Wiene …
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How do I find the kernel of the shift operator in the solution of 2D Ising model?
Okay, this is a second part of my previous question. Again, I'm following Itzykson's book. The fermionic solution for the 2D Ising model is described in terms of a matrix $T = \theta \tilde{\theta}$, …
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Construction of the Klein-Gordon field theory - what is missing?
Many references I know on QFT start the discussion of the Klein-Gordon field theory with some discussion about harmonic oscillators. One such reference is Folland's Quantum Field Theory book. The idea …
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