# 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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### Thermodynamic free energy of interacting system

This question concerns an interacting system's thermodynamic free energy $\Omega$. Generally speaking, The action $S$ for an interacting system has the following form: \begin{equation} S(\phi,\psi) = ...
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### Can the standard Quantum-Mechanical Path Integral also be evaluated on a lattice?

I have been trying to learn about lattice path integrals. Unfortunately, majority of the literature on this topic is in regard to Lattice Quantum Field Theory and Lattice Quantum Chromodynamics. That ...
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### Why must the propagator exponent be imaginary?

In response to asmaier's question, qmechanic showed why the propagator must be $\exp(cS)$. That made perfect sense. But can it also be shown that $c$ is imaginary? I believe it follows from ...
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### How is the free particle propagator derived? [closed]

The free particle propagator is a well known function, for example, see Wikipedia. However, I cannot find a source that explains how to derive the free particle propagator. Please explain how the free ...
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### Momentum Space Propagator from Path Integral Formulation of “Polyakov-style” action for a massive relativistic point particle

I have the derived the following expression for the propagator of a “Polyakov-style” action for a massive relativistic point particle: \begin{equation*} G(X_2 - X_1) = \mathcal{N}'\int_{0}^{\infty}...
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### Multiplicative property of the functional determinant

If we consider two differential operators $\mathcal{D}_1$ and $\mathcal{D}_2$, we can compose them to create the differential operator $\mathcal{D}_1 \mathcal{D}_2$. Then we could consider an action (...
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### Free particle probability to go from $a$ to $b$ [duplicate]

Feynman and Hibbs write that the probability for a particle to go from $a$ to $b$ is \begin{equation*} P(b,a)=|K(b,a)|^2 \end{equation*} The kernel for a free particle is given as \begin{equation*} K(...
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### Fermionic path integral with boundary

Given a path integral: $$K(\eta,\xi) = \int\limits_{\psi(0)=\eta}^{\psi(1)=\xi} e^{\int_0^1\dot{\psi}(t)\psi(t) dt} D\psi\tag{1}$$ where $\psi(t)$ are a real Grassmann fields. I get two answers ... 1 vote
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### Are non-trivial topologies in the gravitational path integral related to large gauge transformations in Yang-Mills?

While the gravitational path integral is not a well-understood concept mathematically, a number of works (particularly in recent research connected to AdS/CFT) emphasize the importance of integrating ...
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### Is the path integral emergent?

I have recently read a couple of papers on lattice QCD and found that there is a well-established connection between Boltzmann distribution and the path integral in QFT (disclaimer: I am not a huge ...
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### What do the authors of the paper mean here exactly by path integral?

First of all, please forgive me if i am asking a dumb question. I don't have a physics background. I was reading this paper by Hawking & Hertog on populating string theory landscape and came ...
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### Is Vacuum Expectation Value equivalent to the sum of Tadpole Diagram in the QFT?

I am recently learning Spontaneously Symmetry Breaking in the QFT. For example let us just focus on the potential $V[\Phi]=a\Phi^2 + b\Phi^4$ where $a<0,b>0$ and denote the vacuum expectation ...
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### Why does the path integral formulation not provide an ontological basis for quantum theory?

I have looked at several books on the foundations of quantum theory and found that the path integral formulation is hardly ever discussed in detail. I find this surprising because this formulation of ...
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### On what space of maps is Polyakov path integral actually defined?

This is a question more concerned about mathematical detail involving the Polyakov path integral. In section $3.2$ of Polchinski's 1st String Theory book it is stated the following about Polyakov path ...
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### General validity of the Linked Cluster Theorem in QFT for arbitrary correlation functions

In QFT, either at zero or finite temperature, the Linked Cluster Theorem (LCT) ensures that all disconnected diagrams appearing in the numerator of the interacting Green's function exactly cancel with ...
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### Path Integral Formalism and Two-Point Function

I'm given an action, $$A[\vec{S}] = \frac{\Theta}{2} \int_{-\infty}^{\infty} dt \left(\frac{d\vec{S}}{dt}\right)^2, \tag{1}$$ with $$\vec{S}^2 = 1.\tag{2}$$ I'm asked to calculate the two point ...
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### Why can a real field have an imaginary saddlepoint?

Suppose we have a functional integral of the form $$\int D\psi \exp\left( -S \right)$$ over a real field $\psi$ with an action $$S=\int_r L(r,\psi(r))=\int_r \frac{1}{2}\psi(r)^2+i\psi(r) j(r).$$ ...
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### Propagator from free scalar path integral

Let $\langle{0|}T\phi(x)\phi(y)|0\rangle$ be the vacuum expectation value of the 2 point correlator for the free scalar field. Page six in these notes say that we can calculate this correlator by ...
1 vote
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### QED photon path (direction of photon emission)

In QED we look at all possible path a photon could go from S to P, and I understand the most significant contributions to the final arrow are the few near straight paths connecting S and P while other ...
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### Inverse square law of a photon in QED

So in Feynman's QED book strange theory of light and matter, he mentioned as a photon travels, it spreads a little, thus the "arrow" shrinks inversely with distance, and that is the inverse ...
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1 vote