# 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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### Does a path integral necessarily mean there is a quantum mechanical description?

Given a path integral for a system $$Z(\phi) = \int [D\phi] e^{-S[\phi]},$$ where I am working in the Euclidean signature, necessarily mean that the system described is quantum mechanical? In the ...
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### Applying the heat-kernel method?

I was wondering if the strategy I am going to try is correct? Am I missing anything important? I am currently trying to apply the stationary phase approximation to a path integral. I need to find the ...
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### One-loop effective action for scalar field on the curved background in large potential

I hope to compute a functional integral $Z=\int \mathcal{D}\phi\,\, e^{-S[\phi]}$ with an action $$S[\phi]=\int d^2x \sqrt{g}\Big((\nabla \phi)^2+\frac{1}{\lambda}M^2(x) \phi^2\Big)$$ The scalar field ...
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### Partition function in quantum field theory

Why does the partition function include current term in free scalar field $$Z[J] = \int \mathcal{D}\phi \, e^{i \left(S[\phi] + \int d^4x \,J(x) \phi(x) \right)}~$$
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### Confusions on expectation value for $\hbar$ going to zero

In Matthew D. Schwartz's QFT book, Chapter 28, the author claims when $\hbar \rightarrow 0$, the following equality (eq 28.4) holds: So how can I see the second "$=$" holds? It seems the ...
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### Examples of path integral where path of extremal action does not contribute the most?

I have learnt that by doing a saddle point approximation in the path integral formulation of quantum mechanics, the classical action (extremal action where $\delta S=0$) is the one that contributes ...
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### Proving that a Wick rotation is valid for a quantum field theory

While trying to find out if there is a rigorous justification for Wick rotating a QFT, I came across this other question (link below ) that mentions the Osterwalder-Schrader Theorem that gives a ...
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### How to deal with integral operators in the action, in the path integral of a field theory?

One could imagine adding to the free action of a scalar field theory some non-local operators given as integrals over the base manifold (or over the boundary) of some smooth function of the scalar ...
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### Confusion regarding a few sign conventions in appyling faraday's law to inductive circuits

In the mit ocw lecture by Prof. Lewin on EMI, He quotes a few statements from here to couple of seconds of the lecture. I am confused why the sign of $L\frac{dI}{dt}$ changes, when we go around and ...
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### Equation of state of a path integral

How does one take the equation of state of a path integral? In "discrete" statistical physics, one has this partition function: $$Z=\sum_{i}\exp(-\beta E[i])$$ And the equation of state is the ...