# Questions tagged [path-integral]

Path integral formulation (Due to Feynman) is a major formulation of Quantum Mechanics along with Matrix mechanics (Due to Heisenberg and Pauli), Wave Mechanics (Due to Schrodinger), and Variational Mechanics (Due to Dirac). DO NOT USE THIS TAG for line/contour integrals.

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### Constraints in path integral and the Lagrange multiplier

I was reading some references on the slave-particle approach to the Kondo problem and Anderson model. It is known that the slave-particle is introduced in the large Hubbard $U$ limit of the system so ...
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### Calculating kernel [closed]

A particle with mass m in one dimension is kept in a constant external force field F.The lagrangian of the system is L=mv^2/2 + Fx.Calculate the kernal if classical action is {[m(xf-xi)^2/2(tf-ti)]+[F(...
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### Generalization of Gaussian integral for tensors

How do you generalize the formula for matrices (or operators) $$\int d^d x \, \exp \Big\{ - \frac{1}{2} x^i A_{ij} x^j \Big\} = \sqrt{\frac{(2 \pi)^d}{\det A}} = \sqrt{\det (2 \pi A^{-1})}$$ for ...
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### Discretization of path integral and linear interpolations

Consider the evaluation by discretization of the path integral $$\int e^{iS[x(t)]}\mathfrak{D}x(t),\quad S[x(t)]=\int_{t}^{t'}\left[\frac{m}{2}\dot{x}(\tau)^2-V(x(\tau))\right]d\tau.$$ One ...
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### Localization Principle (SUSY)

Mirror Symmetry p.200/201 Last section p.200/first p.201 It says, that the localization principle would not work if one would not impose periodic boundary conditions for the fermion integration, ...
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### Fourier transform of matrix element of evolution operator

I learn ''Path integrals in quantum mechanics'' by Jean Zinn-Justin now. There is a chapter about calculating the path integral for particle on a ring (rigid rotator). So, after some calculations we ...
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### Infinite sum: Renormalisation

Trying to do the calculation made in a physics article Real-time Feynman path integral with Picard--Lefschetz theory and its applications to quantum tunneling (page 10 to go from equation 56 to 57), I ...