Recent content by hideelo

To directly answer your question, the idea is that while it reaches a maximal entropy state in a very short time, the space of maximal entropy states is not uniform. They give a measure on the space of states that is defined by how many "simple operations" are needed to get from the initial...

This takes it's origin by ideas promoted by Susskind Maldacena, Swingle, and many others https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.116.191301

If we take the perspective that black holes thermalize (reach maximum entropy) in a very short time and then just sit there and grow in complexity, how do we interpret Hawking radiation in this picture? i.e. you can't just have the state of the black hole keep growing in complexity forever...

I don't think shifting z by anything can help. Suppose you sent z \mapsto z+a for any a then I would get the following -\frac{1}{2}K |z|^2+\bar{J}z \mapsto -\frac{1}{2}K |z+a|^2+\bar{J}(z + a) = -\frac{1}{2}K \left( z\bar{z} + a\bar{z} + z\bar{a} +a\bar{a} -\frac{2\bar{J}}{K} z -...

The integral I'm looking at is of the form \int_\mathbb{C} dz \: \exp \left( -\frac{1}{2}K|z|^2 + \bar{J}z \right) Where K \in \mathbb{R} and J \in \mathbb{C} The book I am following (Kardar's Statistical Physics of Fields, Chapter 3 Problem 1) asserts that by completing the square this...

I think you're saying that the implication does not go the other way. i.e. in my example irreducibility of the U(\omega) representation would not imply irreducibility of the R(\omega) representation. Am I understanding you correctly?

If I have a single spin 1/2 particle, I know that it's total spin in any direction with unit vector can be computed by using the operator σ•n where σ_i are the pauli matrices. Suppose however I had a multiparticle system, is there a generalization of the pauli matrices (which let's call ρ_i) so...

Ok, so my question is "Does an irreducible representation acting on operators imply that the states also transform in an irreducible representation?" and what I mean by that is the following. If I have an operator transforming in an irreducible transformation of some group, I get a corresponding...

Suppose I had some group G, and I could classify all of its irreducible K-representations for some K = R,C, or H. Given that information (how) can I classify its irreducible K-representations for all K. i.e. suppose I knew all the irreducible real representations of G, (how) could I then get...

I am looking at the integral $$\int_0^\infty dx \: e^{-iax} - e^{iax}$$ I know that this does not converge for many reasons, but most obviously because I can rewrite it as $$2i \int_0^\infty dx \: sin(ax) = -2i a [\cos(ax)]_0^\infty$$ which does not converge to anything. However the book...

In general yes, but what I'm doing is in only "pulling out" one creation operator. So while it's true that ## |pq> =a^\dagger(p) a^\dagger(q)|0>## I can then let the ##a^\dagger(q)|0> =|q>## which gives me what I have up there ## |pq> a^\dagger(p) |q>## I think that was OK to do...

The convention I am using (and I think its standard) is that ##a^\dagger(q)## creates a state with momentum q and annihilates a costate with momentum q i.e. $$a^\dagger(q)|0> = |q>$$ and $$<q|a^\dagger(q) = <0|$$ Similarly ##a(q)## annihilates a state with momentum q and creates a costate with...

That's what I thought, but when I worked it out I found no double counting

No, it's the k! that's bothering me

I'm reading Weinberg's QFT volume 1. At the end of section 2.4 he is deriving the Inonu-Wigner contraction where he reduces the Poincaré group to the Euclidean one by taking the low velocity limit. In analyzing how the operators depend on velocity there are some I understand and some I don't. I...