Tagged Questions
1
vote
1answer
29 views
what is the magnetic quadrupole operator?
To find magnetic or electrical moments in quantum theory we must calculate the expectation value of an appropriate operator. the dipoles operator are similar and is easy to find but the magnetic ...
2
votes
0answers
50 views
About deriving the multi-trace index in terms of the single-trace index
This question is in reference to this paper
Combining their equations 5.2, 5.3, 5.6 and 5.7 one seems to be looking at the integral/partition function,
$Z(x) = \prod_{n=1}^{n =\infty}\left [ \int ...
2
votes
0answers
49 views
Helicity for Zero Rest Mass Field Equations
I'm trying to reconcile the usual definition of the helicity operator, namely
$$ h = \hat{p}.S$$
with the definition of a massless helicity $n$ field as a symmetric spinor field $\phi^{A\dots B}$ ...
6
votes
1answer
74 views
Motivation for the Deformed Nekrasov Partition Function
I have recently been doing research on the AGT Correspondence between the Nekrasov Instanton Partition Function and Louiville Conformal Blocks (http://arxiv.org/abs/0906.3219). When looking at the ...
3
votes
1answer
79 views
Transformation law for fermionic measure in functional integral
I am reading the paper "Bosonization in a Two-Dimensional Riemann-Cartan Geometry", Il Nuovo Cimento B Series 11
11 Marzo 1987, Volume 98, Issue 1, pp 25-36, ...
5
votes
1answer
134 views
Is the Hilbert space of $\phi^4$ theory known?
Consider free, real scalar field theory in $d=1+3$ dimensions: $H = \frac{1}{2} \partial_\mu \phi \partial^\mu \phi + \frac{1}{2} m^2 \phi^2$. The Hilbert space of this theory is known; it is just ...
6
votes
1answer
68 views
Are observables associated to spacetime regions?
In the Haag-Kastler approach to axiomatic quantum field theory, it is assumed that observables are 'associated' to spacetime regions. What this actually means is that there is a map $\mathcal{A}: R ...
4
votes
0answers
70 views
Noether currents for the BRST tranformation of Yang-Mills fields
The Lagrangian of the Yang-Mills fields is given by
$$
\mathcal{L}=-\frac{1}{4}(F^a_{\mu\nu})^2+\bar{\psi}(i\gamma^{\mu}
D_{\mu}-m)\psi-\frac{1}{2\xi}(\partial\cdot A^a)^2+
...
0
votes
1answer
75 views
Higher order covariant Lagrangian
I'm in search of examples of Lagrangian, which are at least second order in the derivatives and are covariant, preferable for field theories. Up to now I could only find first-order (such at ...
9
votes
2answers
247 views
Algebraic/Axiomatic QFT vs Topological QFT
Can anybody please tell me a good source investigating the relation between Algebraic/Axiomatic Quantum Field Theory (AQFT) and Topological Quantum Field Theory (TQFT)? Or is there none?
3
votes
0answers
206 views
Mathematics and Physics prerequisites for mirror symmetry [closed]
I am a physics undergrad interested in Mathematical Physics. I am more interested in the mathematical side of things, and interested to solve problems in mathematics using Physics. My current ...
6
votes
1answer
128 views
Are group representations possible when the solution space is not a vector space?
As far as I understand, the motivation for using representation theory in high energy physics is as follows. Assume that a theory has some (internal or external) symmetry group which acts on a vector ...
1
vote
1answer
154 views
What is the mathematical background needed for quantum physics? [duplicate]
I'm a computer scientist with a huge interest in mathematics. I have also recently started to develop some interest about quantum mechanics and quantum field theory. Assuming some knowledge in the ...
4
votes
0answers
94 views
Confused by renormalization [duplicate]
Possible Duplicate:
Suggested reading for renormalization (not only in QFT)
I'm trying to learn QFT. I don't quite understand why renormalization works. If you are calculating a Feynman ...
3
votes
2answers
230 views
Chern-Simons term
In the literature I can only find Chern-Simons terms ( i.e. for a 3-dimensional manifold $A \wedge dA + A \wedge A \wedge A$) for odd-dimensional manifolds. Why can't I write such forms for ...
3
votes
0answers
140 views
What aspects of QFT do mathematicians find troublesome? [closed]
What aspects of "conventional" quantum field theory (i.e. what's used by most practicing physicists) are considered to be lacking mathematical rigor?
3
votes
0answers
61 views
Finding symmetry of a part of an equation, given the group transformation property of another part
I am reading this paper on Dyons and Duality in $\mathcal{N}=4$ super-symmetric gauge theory. The author finds the zero modes or a dirac equation obtained by considering first order perturbations to ...
3
votes
1answer
57 views
Isometry group from information about the center of the group
I am reading this paper on Dyons and Duality in $\mathcal{N}=4$ super-symmetric gauge theory. The author finds the zero modes or a dirac equation obtained by considering first order perturbations to ...
2
votes
2answers
235 views
Intuition for Path Integrals and How to Evaluate Them
I'm just starting to come across path integrals in quantum field theory, and want to get the right intuition for the them from the start. The amplitude for propagation from $x_a$ to $x_b$ is typically ...
3
votes
1answer
190 views
Local and Global Symmetries
Could somebody point me in the direction of a mathematically rigorous definition local symmetries and global symmetries for a given (classical) field theory?
Heuristically I know that global ...
3
votes
0answers
77 views
Isospin and Hypercharge of the SU(2) bps monopole embedding
I am reading the paper Fundamental monopoles and multimonopole solutions for arbitrary simple gauge groups - Weinberg, Erick J .
In appendix C of this paper the author states, that the solution ...
6
votes
1answer
145 views
Equivalent Representations of Clifford Algebra
I'm reviewing David Tong's excellent QFT lecture notes here and am a little confused by something he writes on page 94.
We've considered the standard chiral representation of the Clifford Algebra, ...
1
vote
1answer
167 views
Lorentz Invariant Equation of Motion for Scalar Field
I'm trying to understand why you can't write down a first order equation of motion for a scalar field in special relativity.
Suppose $\phi(x)$ a scalar field, $v^{\mu}$ a 4-vector. According to my ...
8
votes
1answer
279 views
Representations of Lorentz Group
I'd be grateful if someone could check that my exposition here is correct, and then venture an answer to the question at the end!
$SO(3)$ has a fundamental representation (spin-1), and tensor product ...
3
votes
0answers
85 views
Asymptotic limit of the two kink solution of the sine-gordon equation
I am reading a paper on the sine-gordon model. The solution for a two kink solution is given as:
...
5
votes
1answer
171 views
Expectation value calculation for a weird operator
In the paper Fundamental monopoles and multimonopole solutions for arbitrary simple gauge groups.- E weinberg
I am not being able to see one of the calculation. The author states (eqn 3.26)
$$\langle ...
3
votes
0answers
63 views
Divergence calculation of a lie algebra valued quantity having spinor indices
I am reading this paper by E. Weinberg - Fundamental monopoles and multimonopole solutions for arbitrary simple gauge groups.
I am having a problem with a calculation. I don't have much experience ...
1
vote
0answers
72 views
Does the attached “poster” work as a hook into the arXiv paper cited, “Nonlinear Wightman fields”? [closed]
"Nonlinear Wightman fields" are my current response to a wish to do interacting quantum field theory differently, no matter how successful what we currently do may be. The following image of a single ...
2
votes
4answers
302 views
Why the Hamiltonian and the Lagrangian are used interchangeably in QFT perturbation calculations
Whenever one needs to calculate correlation functions in QFT using perturbations one encounters the following expression:
$\langle 0| some\ operators \times \exp(iS_{(t)}) |0\rangle$
where, ...
0
votes
1answer
66 views
What does Friedrichs mean by “Myriotic fields”?
I came across K. O. Friedrichs' very old book (1953) "Mathematical Apsects of the Quantum Theory of Fields", and hardly any of it makes sense to me.
One of the strange things that he refers to are ...
3
votes
2answers
182 views
How do I define time-ordering for Wightman functions?
This is a follow-up question to What are Wightman fields/functions
Ok, so based on my reading, the field operators of a theory are understood to be operator-valued distributions, that is, to be ...
7
votes
1answer
203 views
alternatives to supersymmetry and Coleman-Mandule theorem
Humour me for a minute here and let's imagine that all interesting and plausible supersymmetry models have been "cornered" out by the experimental data;
what sort of alternatives are there for having ...
4
votes
1answer
203 views
What are Wightman fields/functions
Simple question: What are Wightman fields? What are Wightman functions?
What are their uses? For example can I use them in operator product expansions? How about in scattering theory?
4
votes
1answer
308 views
A confusion from Weinberg's QFT text (a vanishing term in Lippmann-Schwinger equation)
I was reviewing the first few chapters of Weinberg Vol I and found a hole in my understanding in page 112, where he tried to show in the asymptotic past $t=−∞$, the in states coincide with a free ...
5
votes
2answers
199 views
Can auxiliary fields be thought of as Lagrange multipliers?
In the BRST formalism of gauge theories, the Lautrup-Nakanishi field $B^a(x)$ appears as an auxiliary variable
$$\mathcal{L}_\text{BRST}=-\frac{1}{4}F_{\mu\nu}^a F^{a\,\mu\nu}+\frac{1}{2}\xi B^a B^a + ...
11
votes
5answers
505 views
Reading list in topological QFT
I'm interested in learning about topological QFT including Chern Simons theory, Jones polynomial, Donaldson theory and Floer homology - basically the kind of things Witten worked on in the 80s. I'm ...
1
vote
1answer
141 views
Problem in Hamiltonian
I need to elaborate the equation ,and need to know what is the physical significance and how matrices will manipulate in the equation $$
\hat{H} = (\hat{\tau_3}+i\hat{\tau_2})\frac{\hat{p}^2}{2m_0}+ ...
2
votes
1answer
186 views
Killing vectors for SO(3) (rotational) symmetry
I am reading a paper$^1$ by Manton and Gibbons on the dynamics of BPS monopoles. In this, they write the Atiyah-Hitchin metric for a two-monopole system. The first part is for the one monopole moduli ...
2
votes
1answer
190 views
Equivalent definitions of primary fields in CFT
I have come across two similar definitions of primary fields in conformal field theory. Depending on what I am doing each definition has its own usefulness. I expect both definitions to be compatible ...
6
votes
2answers
618 views
EM wave function & photon wavefunction
According to this review
Photon wave function. Iwo Bialynicki-Birula. Progress in Optics 36 V (1996), pp. 245-294. arXiv:quant-ph/0508202,
a classical EM plane wavefunction is a wavefunction (in ...
9
votes
3answers
407 views
What areas of physics should a mathematician study to understand TQFT?
I am studying topological quantum field theory from the view point of mathematics.(axiomatic treatise) So it has no explanation about physics. I would like to know physic background of TQFT. But I ...
6
votes
1answer
110 views
precise definition of “moduli space”
I'm curious what the precise definition of the moduli space of a QFT is. One often talks about the classical moduli space, which then can get quantum corrections. Does this mean the quantum moduli ...
6
votes
2answers
91 views
fitting free QFTs into the Haag-Kastler algebraic formulation
Has the free Klein-Gordon quantum field theory been fitted into the
Haag-Kastler algebraic framework? (Actually, John Baez told me "yes", and he should know.) If so, can you describe the basic
...
7
votes
2answers
202 views
Advice on doing physics under the umbrella of mathematics and the converse
In the current scenario of research in QFT and string theory (and related mathematical topics), which of the following would an undergraduate student, like me, be advised to do and why if s/he is ...
4
votes
1answer
202 views
SST (Spin-Statistics Theorem)
Please can you help me understand the SST (spin-statistics theorem)?
How can I prove it from a QFT point of view? how rigorous one can get?
Pauli's proof is in the case of non-interacting fields, how ...
11
votes
2answers
70 views
Discussions of the axioms of AQFT
The most recent discussion of what axioms one might drop from the Wightman axioms to allow the construction of realistic models that I'm aware of is Streater, Rep. Prog. Phys. 1975 38 771-846, ...
6
votes
1answer
159 views
Thermodynamic limit “vs” the method of steepest descent
Let me use this lecture note as the reference.
I would like to know how in the above the expression (14) was obtained from expression (12).
In some sense it makes intuitive sense but I would ...
7
votes
2answers
265 views
Interesting topics to research in mathematical physics for undergraduates
I'm planning on getting into research in mathematical physics and was wondering about interesting topics I can get into and possibly make some progress on.
I'm particularity fond of abstract algebra ...
3
votes
2answers
449 views
What is the symmetry that corresponds to conservation of position?
We know that conserved quantities are associated with certain symmetries. For example conservation of momentum is associated with translational invariance, and conservation of angular momentum is ...
2
votes
1answer
102 views
Spinors in more dimensions and new degeneracies?
As you more than probably know spinors dimensions go as $2^{\frac{D}2}$ in D spacetime dimensions. If we look at the peculiar case of D=2*4, spinors have 4 components and we usually say that's related ...
