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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Quantum to classical mapping: quantum criticality and path integral Monte Carlo

I'm trying to understand the connections between quantum models in d dimensions and classical models in (d+1) dimensions within two, possibly related, contexts: (i) in path integral monte carlo, the ...
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281 views

Potentials in Feynman path integral

I am trying to understand the Feynman path integral by reading the book from Leon Takhtajan. In one of the examples, there is a full explanation of the calculation of the propagator ...
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332 views

Forbidden trajectories in path integrals

In Feynman's path integral formulation we add all the possible trajectories of a particle to get the probability amplitude. What are forbidden trajectories? Not differentiable? Is this related to ...
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152 views

Uncertainty in path integral formulation

In Feynman's path integral formulation, in order to calculate the probability amplitude, we sum up all the possible trajectories of the particle between the points $A$ and $B$. Since we know ...
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1answer
130 views

Path integral formulation understanding [duplicate]

I have done basic quantum mechanics and now I want to do the path integral formulation. I find Feynman's book Path Integrals in Quantum Mechanics difficult. Is there an easier alternative?
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124 views

Path integral representation of $\langle q_f t_f|p(t_1)|q_i t_i\rangle $

How do I calculate path integral representation of $\langle q_f t_f|p(t_1)|q_i t_i\rangle $ where $t_i<t_1<t_f$? I am doing this by discretizing, the time intervals and adding a complete set of ...
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1answer
346 views

Calculation of the spherical harmonic sum in the propagator of the particle on a sphere

I am calculating the propagator of the free particle on a sphere : $K(\theta_f \phi_f t_f; \theta_i \phi_i t_i)$. The wavefunctions in this case are the spherical harmonics $Y_{lm}(\theta, ...
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1answer
209 views

Diagonalizing/eigenvalues of the infinite dimensional matrix of N harmonic oscillators on a ring

I have trying to show that the continuum limit of N quantum harmonic oscillators gives rise the the klein-gordon field. However, instead of a usual finite string, I want to do it on a ring. Hence, my ...
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2answers
475 views

Path Integral Quantization

I was reading through my notes on the path integral quantization of bosonic string theory when a general question about path integral quantization arised to me. The widely used intuitive explanation ...
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338 views

Differential equation (Greens function) satisfied by the kernel using path integrals

I'm reading Feynman and Hibbs, Quantum Mechanics and Path Integrals. How do I show that the kernel $$\tag{2-25} K(x_2 t_2;x_1 t_1)=\int e^{\frac{i}{\hbar}S[2,1]}\mathcal{D}x$$ satisfies the ...
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355 views

Calculating the the kernel using path integrals for quadratic lagrangians

I am reading Feynman and Hibbs on Path Integrals. In section 3.5, they show that the kernel for a lagrangian of the form $L=a(t)\dot{x}^2+b(t)\dot{x}x+c(t)x^2+d(t)\dot{x}+e(t)x+f(t)$ is ...
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510 views

Is every quantum measurement reducible to measurements of position and time?

I am currently studying Path Integrals and was unable to resolve the following problem. In the famous book Quantum Mechanics and Path Integrals, written by Feynman and Hibbs, it says (at the beginning ...
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152 views

$\langle B|A \rangle$ expressed in terms of the Partition Function

Say you have an electron departing from point A and reaching poing B after a time t. According to some helping friend, the Partition Function for that electron going from point A to B can be written ...
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1answer
318 views

Which is this formula Feynman talks about in the QED book?

I am reading the fantastic QED Feynman book. He talks in chapter 3 about a formula he considers too complicated to be written in the book. I would like to know which formula he talks about, although I ...
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1answer
228 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 ...
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191 views

Path Integrals Page Peskin

Hi this problem relates directly to path integrals but I imagine it is a maths trick that I am missing. One has an expression such as $$\int dx \exp\left[i\frac{(p)^{2}}{2}-iV(\frac{f}{4})\right] $$ ...
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647 views

Physical Interpretation of the Integrand of the Feynman Path Integral

In quantum mechanics, we think of the Feynman Path Integral $\int{D[x] e^{\frac{i}{\hbar}S}}$ (where $S$ is the classical action) as a probability amplitude (propagator) for getting from $x_1$ to ...
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1answer
77 views

Path integral with boundary and bulk terms

I was wondering if their is a general strategy for computing path integrals with a mix of boundary and bulk integral actions. Do people use divergence theorem to convert the action into bulk ...
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610 views

What is the path integral exactly?

I asked a question here about path integrals and QFT. I just want to confirm something. Is the path integral in quantum field theory a mathematical tool only? I thought the path integral meant that ...
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3answers
625 views

Quantum field theory, particle interpretations and path integrals?

I am trying to find some names or models of a particle interpretation of quantum field theory which isn't a literal path integral approach? Are there any particle interpretations of quantum field ...
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576 views

When does $\hbar \rightarrow 0$ provide a valid transition from quantum to classcial mechanics? When and why does it fail?

Lets look at the transition amplitude $U(x_{b},x_{a})$ for a free particle between two points $x_{a}$ and $x_{b}$ in the Feynman path integral formulation $U(x_{b},x_{a}) = \int_{x_{a}}^{x_{b}} ...
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826 views

Why path integral approach may suffer from operator ordering problem?

In Assa Auerbach's book (Ref. 1), he gave an argument saying that in the normal process of path integral, we lose information about ordering of operators by ignoring the discontinuous path. What did ...
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817 views

How would a Lagrangian be used to recover the Schrodinger equation?

I heard that the Lagrangian is defined in the path integral formulation of quantum mechanics. How would the Lagrangian in this formulation be used to recover the Schrodinger equation that we normally ...
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1answer
291 views

Is the following a simpler viable alternative to Feynman's interpretation of the double slit experiment

Feynman suggested that there is an infinity of trajectories for a single electron travelling from the source to the phosphorescent screen. He said that one electron goes through both holes (Fig 4.10, ...
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path integrals: how/why can the phase be identified with the action?

In Peskin & Schroeder, chapter 9 introduces the functional methods. The idea, to recall, is simply to sum over all the possible paths: $U(x_a,x_b;T) = \sum_{\text{all paths}} e^{i . ...
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624 views

What's the role of classically forbidden paths in path integral?

I'm interested in how and how much classically-forbidden paths contribute to a path integral? Is there any good reference on the issue? Any discussion in QM or QFT context would be appreciated. ...
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463 views

Can path integrals be used to understand entanglement?

I like path integrals. I prefer to try to understand quantum phenomena in terms of path integrals rather than Hamiltonian mechanics. However, most of the standard texts on quantum mechanics start from ...
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694 views

Change of variables in path integrals

I need to evaluate a path integral which involves a set of fields $X=\left\{ \psi_i \right\}$: $$ I = \int \prod_i \mathcal{D} \psi_i e^{-S \left[ \left\{ \psi_i \right\} \right] } $$ In order to ...
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674 views

Intuition for Path Integrals and How to Evaluate Them

I'm just starting to come across path integrals in quantum field theory, and want to get the right intuition for the them from the start. The amplitude for propagation from $x_a$ to $x_b$ is typically ...
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1answer
163 views

Inclusion of information about external particles to calculate scattering amplitudes

In this (schematic) equation to calculate the scattering amplitude A by integrating over all possible world sheets and lifetimes of the bound states $$ A = \int\limits_{\rm{life time}} d\tau ...
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1answer
449 views

What is the value of a quantum field?

As far as I'm aware (please correct me if I'm wrong) quantum fields are simply operators, constructed from a linear combination of creation and annihilation operators, which are defined at every point ...
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376 views

Path integral with zero energy modes

Consider the field integral for the partition function of a free non-relativistic electron in a condensed matter setting, i.e. $$ Z = ∫D\bar\psi D\psi \exp\left(-\sum_{k,ω} \bar\psi_{k,ω} (-iω + ...
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The meaning of imaginary time

What is imaginary (or complex) time? I was reading about Hawking's wave function of the universe and this topic came up. If imaginary mass and similar imaginary quantities do not make sense in ...
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Gaussian Integrals : Functional determinant expressed as a trace

Be $A_{ij}$ a symmetric matrix. Then I can easily write $$ \int \exp\left(-\frac{1}{2}\sum_{i,j}x_i A_{ij} x_j+\sum_{i} B_i x_i\right)\; d^nx= \sqrt{(2\pi)^n}\exp\left\{-\frac{1}{2}\mathrm{Tr}\log ...
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Quantum mechanics textbooks that use path integrals

I'm looking for a textbook in quantum mechanics that relies heavily on Green functions and the path integral formalism to supplement my QM books. I want to do some calculations using alternative ...
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249 views

What is the relationship between consistent histories and path integrals?

As can for example be learned from chapter I.2 of Anthony Zee's Quantum field theory in a nutshell, path integrals can be used to to calculate the amplitude for a system to transition from one state ...
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541 views

Path integral and geometric quantization

I was wondering how one obtains geometric quantization from a path integral. It's often assumed that something like this is possible, for example, when working with Chern-Simons theory, but rarely ...
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363 views

Chemical reaction as state transition?

When considering diffusion of chemicals, the reaction part is business of chemical kinetics, where the relevant characteristics of different substances come from collision theory together with some ...
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266 views

Importance of phase in probability amplitude in QFT

I have started teaching myself QFT from the textbook by A. Zee. From reading that book, my idea of a path integral in field theory is the probability amplitude to go from a given field configuration ...
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220 views

classical dynamics on group manifold SU(2)

I am trying to understand how to formulate classical dynamics on group manifold SU(2). This will be an exercise for me to the more advanced subject of path integral on group manifold. Does someone ...
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150 views

Calculating equation of motion using path integral

Suppose my action integral is $S=\int d^4x(\nabla \times A)^2$ and $\delta S$ gives $\delta S =\int d^4x [2(\nabla \times A).(\nabla \times \delta A)]$ I would like to calculate the coefficient of ...
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2answers
835 views

Free Particle Propagator Using Path Integrals

I'm trying to recreate some work that a professor explained to me in his office, specifically deriving the free particle propagator going from $(y,0)$ to $(x,T)$ using the Feynman Path Integral. I'm ...
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384 views

Surface terms for field path integrals?

My question relates to something that I´ve seen in many books and appears in all its glory here: Ryder, pg 198 My question is about eq. 6.74. Which I repeat below: $$i \int {\cal D}\phi \frac{\delta ...
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1answer
462 views

Classical limit of the path integral formulation of quantum mechanics

It is well-known that if $S \gg \hbar$, then the classical path dominates the Feynman path integral. But is there some to show that if $S\gg\hbar$, then the particle's trajectory will approach the ...
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1answer
358 views

Why can't the functional integral be derived in a mathematically rigorous way?

Why can't the functional integral be derived in a mathematically rigorous way? What are the obstacles that we have to overcome in order to achieve that goal?
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444 views

Relation between Dirac's generalized Hamiltonian dynamics method and path integral method to deal with constraints

What is the relation between path integral methods for dealing with constraints (constrained Hamiltonian dynamics involving non-singular Lagrangian) and Dirac's method of dealing with such systems ...
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469 views

Does the vacuum energy problem of quantum field theory only occur in the Hamiltonian approach, or also in the path integral approach and in AQFT?

In a standard QFT class, you're being indoctrinated that there is the "infinite vacuum energy density problem". (This is sometimes paraphrased as the "cosmological constant problem", which is in my ...
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How can there be a quantum field theory that predicts all particle masses?

Say I have a theory with only one (energy) scale, e.g. one given by the fundamental constants $$\epsilon=\sqrt{\dfrac{\hbar c^5}{G}}.$$ In this case, where I can't compare to something else, is ...
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568 views

Discrete version of Feynman path integrals

I've decided to put a very limited amount of my time into understanding the path integral formulation of quantum mechanics. I'm interested in the mathematical formalism more than the physics, so I'd ...
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307 views

Integrating over a gauge field in the field integral formalism

I'm currently trying to study a chapter in Altland & Simons, "Condensed Matter Field Theory" (2nd edition) and I'm stuck at the end of section 9.5.2, page 579. Given the euclidean Chern-Simons ...