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Results tagged with path-integral
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user 36793
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.
1
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Why does spin appear in quantum systems but not classical systems?
The title of the question is not quite correct. I offer a a partial answer and I hope it helps to some extent! I might expand it a bit later.
The way the angular momentum is first defined in classica …
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6
votes
2
answers
2k
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Why does the classical path give the dominant contribution in the path integral?
Why is it that the classical path gives the dominant contribution in the quantum mechanical path integral? How do we understand this?
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9
votes
3
answers
2k
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How to integrate out the $W$-boson fields?
What does it mathematically mean to 'integrate out' the $W$-boson fields to obtain the Fermi Lagrangian from the electroweak theory? How does one achieve this mathematically? It will be helpful if som …
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30
votes
3
answers
4k
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In what sense is the proper/effective action $\Gamma[\phi_c]$ a quantum-corrected classical ...
There is a difference between the classical field $\phi(x)$ (which appears in the classical action $S[\phi]$) and the quantity $\phi_c$ defined as $$\phi_c(x)\equiv\langle 0|\hat{\phi}(x)|0\rangle_J$$ …
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14
votes
1
answer
744
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What are the minimal postulates to do quantum mechanics in path-integral formulation without...
I ask this question because many of the books I'm familiar with assumes a familiarity with the operator formulation and then develops the path-integral formulation partly based on a mixture of operato …
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2
votes
Accepted
Expectation values in a quantum field theory
I think the path integral approach provides an answer. In terms of the normalized generating functional $\mathcal{Z}[J]=\frac{Z[J]}{Z[0]}$, the expectation value is given by $$\langle 0|\phi(x)|0\rang …
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3
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Expectation values in a quantum field theory
Consider a quantum field $\phi(x)$ (say, a scalar) at a spacetime location $x$. It turns out that $$\langle\phi(x)\rangle_0\equiv\langle 0|\phi(x)|0\rangle=0.\tag{1}$$ This is easily obtaied by using …
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0
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2
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465
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What is a symmetry in the path-integral formulation of non-relativistic quantum mechanics?
Suppose $\mathbb{U}$ is a unitary operator acting on the Hilbert space of states representing a symmetry transformation such as rotation, translation, etc. $\mathbb{U}$ is said to be a symmetry of non …
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12
votes
3
answers
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Why is there no anomaly when particle mechanics is quantized?
We know that if one or more symmetries of the action of a classical field theory is violated in its quantized version the corresponding quantum theory is said to have anomaly.
Is this a sole featur …
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3
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Particle creation by a source as explained in A. Zee's QFT in a Nutshell
For the free theory $$W[J]=-\frac{1}{2}\int\int d^4x d^4y J(x)D(x-y)J(y)\tag{1}.$$ Introducing the Fourier transform, $J(x)\equiv \int d^4k e^{+ik\cdot x}\tilde{J}(k)$, we get, $$W[J]=-\frac{1}{2}\int …
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0
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1
answer
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Value of vacuum-to-vacuum transition amplitude in absence of the source $j(x)$
The quantity $Z[j]=\int D\phi\exp[iS[\phi,j]]$ represents the vacuum-to-vacuum transition amplitude in presense of an external source $j(x)$. Shouldn't the quantity $Z[0]$ i.e., the vacuum-to-vacuum t …
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3
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1
answer
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Deriving the equality $\frac{\delta \Gamma[\phi_c]}{\delta\phi_c(x)}=0=\langle 0|\frac{\delt...
I'm trying to convince myself that $$\Gamma[\phi_c]=W[J]-\int d^4x\hspace{0.2cm} j(x)\phi_c(x)$$ is the effective action i.e., it contains all quantum corrections to the classical action $S[\phi]$.
…
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3
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Vacuum to vacuum transition amplitude confusion
I think this is a good question and need to be addressed because this is very often not explained well in books.
The notation $|0,\pm\rangle_j$ has no meaning. But the expression, $(\langle 0,+\inft …
- 27.2k
5
votes
1
answer
990
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Particle picture in the path-integral formulation of Quantum Field Theory
In canonical quantization, the particles arise as quantized excitations on the vacuum $|0\rangle$. For example, a one-particle state with four momentum $p=(E,\textbf{p})$ is given by $$|p\rangle\sim a …
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8
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2
answers
2k
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Understanding typical non-perturbative calculations in QFT [closed]
Perturbative calculations in quantum field theory are based on S-matrix expansion and calculating the Feynman diagrams. These Feynman diagrams are related to the scattering cross-sections and decay ra …
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