Tagged Questions

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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Determinant of a propagator

Say I have a path integral $\int D \phi \exp(i S_0)$. $S_0$ is the usual free action $$S_0=\frac{1}{2}\int\phi (-\Box-m^2) \phi=\frac{1}{2}\int \phi G^{-1} \phi,$$ and at the moment I'm not ...
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Double slit interference pattern with path integral

I need to calculate the classical action of a particle going trough a double slit and interfering at a wall on a certain position (x,y). Any hint on how to do that?
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Lagrangian vs Hamiltonian and symmetry of a theory

It is said that since the path-integral formulation of quantum mechanics/or quantum field theory uses the Lagrangian rather than the Hamiltonian, as the fundamental quantity, it preserves all the ...
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How to deal with boundary conditions for path integrals?

For non-relativistic quantum mechanics, the boundary conditions are rather simple to deal with, they are just \langle x_1, t_1 \vert x_2, t_2\rangle = \int_{x_1(t_1)}^{x_2(t_2)} ...
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Once a quantum partition function is in path integral form, does it contain any operators?

Once a quantum partition function is in path integral form, does it contain any operators? I.e. The quantum partition function is $Z=tr(e^{-\beta H})$ where $H$ is an operator, the Hamiltonian of the ...
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Equivariant cohomology formula

I'm studying equivariant cohomology on three references: Szabo's review about equivariant localization (S); Libine's note on equivariant cohomology (L); Berline, Getzler, Vigne's book "Heat Kernels ...
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How can I understand the tunneling problem by Euclidean path integral where the quadratic fluctuation has a negative eigenvalue?

I came across the S. Coleman's seminal papers 'Fate of the false vacuum' (http://dx.doi.org/10.1103/PhysRevD.15.2929, http://dx.doi.org/10.1103/PhysRevD.16.1762) where he describes the tunneling ...
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recovering numerical wave function using path integral after Wick rotation

I have written two different path-integral codes, PATHINT and PATHTREE, to numerically solve some classical-physics problems in nonlinear systems, finance and neuroscience. They work just fine. My ...
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What is the connection between Hilbert Space and path integrals?

Given a space of states $|\rangle$, $|x\rangle$, $|x,y\rangle$, with the creation operators such as $\hat{\phi}(x)|y,z\rangle=|x,y,z\rangle$ for creating a particle at position $x$ and so on. How ...
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Least Action Principle (Classical and Quantum Theory)

I) My first question would be "why should classical systems obey the principle of least action ?" When we find out the propagator in quantum physics, we find the amplitude to be equal to the sum over ...
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How do instantons look in real time/spacetime?

Instantons, as I understand it, are mathematical constructions in Eucledean spacetime. Does it imply that instantons do not exist in real spacetime or instanton tunneling effects are does not have ...
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General formula for expanding wave function in terms of orthogonal states?

Given a wave function $\psi(x) = \langle \psi | x \rangle$. It can be expanded in terms of orthogonal states: $$\langle \psi | x \rangle = \sum_n \langle \psi | n \rangle \langle n |x \rangle$$ ...
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How to separate an exponential with a Hamiltonian with both momentum and position operators?

Statement of exercise On a page 11 of A.Zee's book QFT in a Nutshell, he derives Dirac's formulation of the path integral formulation of QM for a free particle. This starts with the free particle ...
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What is Hawking Hartle vacuum state and why does the following Euclidean path integral gives the wave functional of it?

I am studying the wave function of black hole via the paper by Sergey Solodukhkin, Entanglement entropy of black holes,arXiv:hep-th: 1104.3712. In the paper, equation (53) is as follows: ...
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Regularization of the 1-dimensional Laplacian

Disclaimer: this is a technical question about regularization of functional determinants which comes from a person with (relatively) strong background in QFT, string theory and path integrals, who ...
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How exact is the analogy between statistical mechanics and quantum field theory?

Famously, the path integral of quantum field theory is related to the partition function of statistical mechanics via a Wick rotation and there is therefore a formal analogy between the two. I have a ...
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Path integral approach of QFT: Concept of particle

How does one introduce the concept of creation and annihilation of particles in the Path integral formulation of quantum field theory? In Canonical quantization, particles are excitations on the ...
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Chern-Simons function

The Chern-Simons function on the space of connections, mod the gauge transformations, on a 3-manifold can be defined by an integral. I study mathematics as profession, so I want to know what is the ...
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Path Integral Evaluation

I've seen the path integral formulation now in a couple contexts (propagator in quantum mechanics, and coherent state functional integral in many body physics). I'm now struggling with how to actually ...
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In M. Nakahara's book Geometry, Topology and Physics on page 19, the probability amplitude for a particle to move from $x_i$ at time $t_i$ to $x_f$ at time $t_f$ is given as $$\tag{1} \langle x_f, ... 1answer 82 views Harmonic Oscillator propagator I'm reading the book on Quantum Field Theory by Anthony Duncan, and I'm a little lost with something of propagators. He first define the propagator K(q_f,T;q_i,0) as the amplitude of detecting a ... 3answers 1k views The path integral and Feynman diagrams This question is somewhat of a historical one, but it also contains some physics. I am curious to find how exactly the concept of Feynman diagrams arose (I assume from Feynman's path integral)? The ... 0answers 59 views Path Integral Simulation I am trying to do a simulation with path integrals. I previously simulated with a step potential by time evolving the eigenvectors of the Hamiltonian. See code and video. Notice is is a bit weird, ... 1answer 156 views What is the relation between phase space formulation with Wigner quasi-probability distributions and path integral formulation of quantum mechanics? I am trying to conceptually connect the two formulations of quantum mechanics. The phase space formulation deals with Wigner quasi-probability distributions on the phase space and the path integral ... 0answers 28 views Lattice propagator computation I am reading this lecture on random surface theory by Thordur Jonsson. I feel like I should describe the problem a little for those who don't want to read the lecture. We are ultimately interested in ... 2answers 275 views Discretization of action in path integral I am reading Peskin and Schroeder (path integrals) and it states that discretising the classical action gives:$$S~=~\int \left(\frac{m}{2}\dot{x}^{2}-V(x)\right) dt ~\rightarrow~ \sum ...
In quantum gravity it is generally said that the partition function is written as: $$Z[J] = \int e^{ i S[g] +J.g } D[g]$$ My question is why do we functionally integrate over all possible metrics ...