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Results tagged with quantum-field-theory
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user 71434
Quantum Field Theory (QFT) is the theoretical framework describing the quantisation of classical fields which allows a Lorentz-invariant formulation of quantum mechanics. QFT is used both in high energy physics as well as condensed matter physics and closely related to statistical field theory. Use this tag for many-body quantum-mechanical problems and the theory of particle physics. Don’t combine with the [quantum-mechanics] tag.
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Why care that 1-particle states $a^{\dagger}_{\mathbf{p}}|0\rangle$ have $\langle\mathbf{p}|...
When defining momentum eigenstates, Peskin+Schroeder (in Chapter 2) define
$$
|\mathbf{p}\rangle = \sqrt{2E_\mathbf{p}} a^{\dagger}_{\mathbf{p}}|0\rangle.
$$
The prefactor of these states $\sqrt{2E_\m …
- 213k
1
vote
1
answer
75
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Time ordered correlator from path integral: equation of motion?
Consider a Lagrangian $L(\phi)$ for a field $\phi$ (assume it is a free real scalar for simplicity). Then the time ordered propagator can be expressed as a path integral
$$
\langle\Omega|T\{ \phi(x) \ …
- 213k
3
votes
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Use the commutation relation to show that the conjugate momentum acts on eigenstates of $\ha...
This is part (b) of Schwartz's Problem 14.3 in his Quantum Field Theory and the Standard Model textbook.
Suppose that we have a real scalar field operator $\hat{\Phi}(x^0,\mathbf{x})$ with conjugate m …
- 94
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vote
Accepted
Interaction hamiltonian of Unruh-De Witt detector in Schrödinger picture
In your free Hamiltonian $H_0$ you need a factor $\frac{d\tau}{dt}$ in front of the qubit term (but not the field term) which makes sure the $H_0(t)$ generates time translations in Minkowski time for …
- 3,764
2
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1
answer
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Schroeder's Minkowski Space Integral - Concerns about Wick Rotations
In the Appendix of Peskin & Schroeder's "An Introduction to Quantum Field Theory" there is a list of integrals in Minkowski space. Of particular interest to me is the integral (A.44):
$$
I(\Delta) = \ …
- 213k
3
votes
0
answers
247
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Out-Of-Time-Correlators for free and interacting field theories
Consider the Out-Of-Time-Correlator (OTOC)
$$
\mathrm{Tr}\left[ - [ \phi(t,\mathbf{x}) , \phi(t',\mathbf{x}') ]^2 \rho\ \right]
$$
where $\rho$ is some initial density matrix, and $\phi$ is a quantum …
- 2,666
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votes
2
answers
956
views
Cutoff-Scheme Renormalization and Order of Integration in QFT
The following is the result of Fubini's Theorem, describing when you can replace a double integral with an iterated integral safely:
For a set $X \times Y \subset \mathbb{R}^2$, if $\iint |f(x,y)| d( …
- 8,900
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votes
1
answer
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Does the Fock space for a free QFT decompose into a tensor product of Fock spaces for each m...
Take a free relativistic QFT, say for a real scalar field $\phi$ with the Lagrangian density
$$
\mathscr{L} = \frac{ \partial_{\mu} \phi \partial^\mu \phi - m^2 \phi^2}{2} \ .
$$
After quantization we …
- 4,421
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votes
1
answer
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QFT and divergences: what makes the finite part be regularization-independent?
It seems that the "finite part" of divergent loop integrals are the same, irrelevant of the regularization scheme used to regulate the integrals - why is this?
Consider the following momentum-space in …
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1
answer
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For real scalars $\phi$ and $\partial_t \phi = \pi$, why can't the Hamiltonian have terms of...
Suppose one has a real scalar field $\phi$ and its conjugate momentum field $\pi := \partial_t \phi$. If the scalar is free and using metric $(-+++)$, the action is
$$
\int d^4x\ \mathscr{L}_{\mathrm{ …
- 1,337
0
votes
1
answer
151
views
Schrodinger versus Interaction Pictures for Mukhanov Field $\hat{v}(\eta,\mathbf{x})$ in inf...
EDIT: This is more than anything else, a question about how to define Schrodinger-picture operators, if you are given an Interaction picture set of operators (with a time-dependent potential: in this …
- 1,017
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votes
1
answer
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Matsubara Field Theory - what does imaginary time $\tau$ in $G(\tau,\mathbf{x})$ mean?
Consider the free, real scalar field $\phi$ in Matsubara Finite-Temperature quantum field theory, where our system is kept in equilibrium with a heat bath at temperature $\frac{1}{\beta}$.
Then the f …
- 213k
6
votes
1
answer
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For Hawking radiation, is the scalar field $\phi$ assumed to be in the Unruh vacuum state?
In Hawking's paper "Particle Creation by Black Holes" I'm not really able to pick apart what vacuum state Hawking is assuming the field $\phi$ to be in.
The paper "Hawking radiation as perceived by di …
- 55k
4
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answers
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Massive versus Massless $\phi^4$ Sunset Diagram - does $\frac{1}{\epsilon^2}$ term vanish fo...
In a real scalar massive $\phi^4$-interacting theory consider the amputated sunset diagram. This is the integral out of Kleinert and Schulte-Frohlinde Critical Properties of $\phi^4$-Theories:
The a …
- 213k
5
votes
0
answers
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What motivates the definition of the Klein-Gordon Inner Product? [duplicate]
I am following along Marc Casal's lecture slides "Quantum Field Theory in Curved Spacetime". For scalar functions $f$ and $g$ we define the Klein-Gordon inner product as follows:
$$
\langle f,g \rangl …
- 3,764