Recent content by youngurlee

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 $$...

thank you.

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.

How could you apply Stokes' theorem in n D for 1-form but not (n-1)-form? Is it valid for all k-forms, where k<n?

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...