State space of QFT,CCR and quantization,spectrum of a field operator?
In the canonical quantization of fields, CCR is postulated as (for scalar boson field ):
[ϕ(x),π(y)]=iδ(x−y) ------ (1)
in analogy with the ordinary QM commutation relation...
Spontaneous symmetry breaking: the vacuum be infinitly degenerate?
In classical field theories, it is with no difficulty to imagine a system to have a continuum of ground states, but how can this be in the quantum case?
Suppose a continuous symmetry with charge Q is spontaneously broken, that...
The time reversal operator T is an antiunitary operator, and I saw T^\dagger in many places
(for example when some guy is doing a "time reversal" THT^\dagger),
but I wonder if there is a well-defined adjoint for an antilinear operator.
Suppose we have an antilinear operator A such that
$$...
lugita15, I know little about Lebesgue integral.
Be it a Lebesgue integral, interchange of derivative and integral is always allowed ?
I read somewhere that Lebesgue integral is a generalization of Riemann integral, then if the interchange in Riemann integral does not hold for a certain...
thank you for your reply, but I really think some condition is required.
for example, look upon \langle f| (independent of t) as a eigenbra of F whose eigenbras are continuous in f. and \langle f| acts on |\psi\rangle as an linear functional.
that is:
\langle f|\psi\rangle=\psi...
The general evolution of a ket |\psi\rangle is according to
-i\hbar\frac{d}{dt}|\psi\rangle=H|\psi\rangle
without specifying a representation.
From this equation, how can you simply get a equation in a certain representation F as below:
-i\hbar\frac{\partial}{\partial t}\langle...
vanhees71, thank you for your reply.
Your method is exactly what I mean by solving it using the propagator U(t) in terms of P's eigenbras and eigenkets.
What I wonder is why can't I solve it in coordinate space.
For example, after infinitesimal interval \Delta t, by...
my question comes thus:
suppose we set up a device to detect a particle, it can detect the particle when the particle occur with in the region [a,b],
so when the device really detected the particle, the wave function of the particle must collaspe to one vanishes without the region, in a special...
for a 1D free particle with initial wave function \phi(x') square shaped(e.g. \phi(x')=1,x'\in [a,b],otherwise it vanishes),
my question is: how does it evolve with time t?
if we deal with it in P basis, it is easily solved, using the propagator U(t)=∫|p'><p'|e^{-\frac{ip'^2...
You're right, I saw this claim in "Multivariate Calculus" by Alder(see the attached).
I know not the detail, but I feel that the validity of such a claim is just what I want.
Oh, I am wrong, I messed up Stokes' theorem.
Stokes theorem applies to (n-1)-form in n D, not for all k-forms with k<n.
It seems that my problem remains unsolved.
actually the order of dx_{i}\wedge dx_{i} isn't of much importance, and hence the cyclic behavior or some other. one can always get a desired order, since the coefficients of the basic 2-forms can be made opposite in step.
The exterior derivative defined by d\omega=dg_1\wedge dx^1+\cdots+dg_n\wedge dx^n=(\partial_1g_1dx^1+\cdots+\partial_ng_1dx^n) \wedge dx^1+\cdots+(\partial_1g_1dx^1+\cdots+\partial_ng_1dx^n) \wedge dx^n is all right (I found it in a lecture document), so according to \int_{\partial...