h******y
发帖数: 26 | 1 Some friend asked me the following question:
For a real scalar field \phi, assume that H = H_free - \int d^3\ x J \phi. J
(x, t) is just some real number, source, or background field, without second
quantization. Now, what is the amplitude \psi(x, t) for finding a particle
at time t(before, during, or after source is on/off) at position x? The J(x,
t) is nonzero only for finite period of time. And the initial state is
vacuum, when t --> -\infty
This question looks simple. However, I cannot find | d****y
发帖数: 53 | 2 Why do you worry about Lorentz invariance here? J(x,t) breaks time
translation symmetry anyway. Also what's the worry about causality here?
If you mean unitarity, here you are using Hamiltonian rather then Lagrangian
formulation, so unitary is there by default. If you mean causality, we are
doing quantum mechanics in flat spacetime, how could there be any issue with
causality?
Just write down the initial wave function as superposition of plane waves.
Compute the transition amplitude, maybe in pe | m**********e
发帖数: 12525 | 3 你去看functional quantization, page 282-292,
an introduction to quantum field theory
J
second
particle
x,
satisfie
【在 h******y 的大作中提到】
: Some friend asked me the following question:
: For a real scalar field \phi, assume that H = H_free - \int d^3\ x J \phi. J
: (x, t) is just some real number, source, or background field, without second
: quantization. Now, what is the amplitude \psi(x, t) for finding a particle
: at time t(before, during, or after source is on/off) at position x? The J(x,
: t) is nonzero only for finite period of time. And the initial state is
: vacuum, when t --> -\infty
: This question looks simple. However, I cannot find
| m**********e
发帖数: 12525 | 4 是有这个问题,所以要加上时序
Lagrangian
are
with
oscillator
【在 d****y 的大作中提到】
: Why do you worry about Lorentz invariance here? J(x,t) breaks time
: translation symmetry anyway. Also what's the worry about causality here?
: If you mean unitarity, here you are using Hamiltonian rather then Lagrangian
: formulation, so unitary is there by default. If you mean causality, we are
: doing quantum mechanics in flat spacetime, how could there be any issue with
: causality?
: Just write down the initial wave function as superposition of plane waves.
: Compute the transition amplitude, maybe in pe
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