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Results tagged with second-quantization
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user 36793
Second quantization or canonical quantization in quantum field theory and many-body systems is the collective organizing and accounting of an infinity of quantum excitations and their interactions through quantum field operators.
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Equal time commutation relations in canonical quantization of relativistic free fields
Let me sketch an answer elaborated in the reference A First Book of Quantum Field Theory by Lahiri and Pal (Second edition, Page $30$).
According to this reference above, the commutator $$[\phi(t,\t …
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Can the mass term be responsible for creation and destruction of particles?
In an interacting quantum field theory, for example, QED, the Dirac mass $m\bar{\psi}\psi$ is a piece of the free Dirac Lagrangian. On the other hand, the interaction term $j^\mu A_\mu=e\bar{\psi}\gam …
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What is a quantum number in a quantum field theory?
In non-relativistic quantum mechanics, quantum numbers are associated with eigenvalues of an operator. For example, $\ell$ is a quantum number associated with the eigenvalue $\ell(\ell+1)\hbar^2$ orbi …
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The Schrödinger equation as an Euler-Lagrange equation
In section 1.2 on p. 14 in the book Many-Particle Physics by Gerald D. Mahan, he points out that the Schrödinger equation in the form
$$i\hbar\frac{\partial\psi}{\partial t}~=~\Big[-\frac{\hbar^2\nabl …
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answer
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Basic understanding of the Fock space of a quantized real scalar field
The states in quantum mechanics belong to some Hilbert space while the states in quantum field theory belong to a Fock space. For simplicity, let me stick to the Fock space emerging after the quantiza …
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Connection between the 'spin' and 'polarization' of relativistic and non-relativistic particles
Context 1 The spin $s$ of a relativistic particle of mass $m$ can be read off from the eigenvalue $s(s+1)$ of the operator $-
\frac{W_\mu W^\mu}{m^2}$ in the rest frame of the particle where $W^\mu=\f …
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What are the spins of Goldstone bosons in Condensed matter systems
In Condensed Matter systems, acoustic phonons and magnons are two famous examples of the bosonic quanta of Goldstone modes.
Question What are their spins? Has it been measured in experiments?
So …
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How will the (anti)commutation relation between two different fermion fields look like? [duplicate]
The anti-commutation relation between the components of a fermion field $\psi$ is given by $$[\psi
_\alpha(x),\psi_\beta^\dagger(y)]_+=\delta_{\alpha\beta}\delta^{(3)}(\textbf{x}-\textbf{y}).$$
In …
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vote
1
answer
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Can localized wavepackets have mass?
Page 31 of David Tong's notes on QFT (also in Srednicki's book while discussing LSZ reduction formula), talks about Gaussian wavepackets $$|\varphi\rangle=\int \frac{d^3\textbf{p}}{(2\pi)^{3}}e^{-i\te …
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1
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Quantization prescription for an interacting field theory
To my understanding, unlike free fields, interacting fields cannot be expanded in terms of Fourier modes, with the Fourier coefficients representing creation and annihilation operators. Then is it pos …
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Dirac equation in QFT vs relativistic QM
How does the Dirac equation in quantum field theory solve the existing problems in the interpretation Dirac equation (as a single-particle wave equation) in relativistic quantum mechanics?
EDIT: The …
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Equal time commutation relations in canonical quantization of relativistic free fields
Why is equal time commutation relation used in canonical quantization of relativistic free fields? In a relativistic theory, space and time are to be treated on equal footing.
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