Quantum Field Theory (QFT) is the theoretical framework describing the quantisation of classical fields which allows a Lorentz-invariant formulation of quantum mechanics. QFT is used both in high energy physics as well as condensed matter physics and closely related to statistical field theory. Use ...

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Lorentz-invariance of step function

I was reading about the Lorentz invariant integration measure $\int \frac{d^3k}{2E_K}$, and ways to prove that this was Lorentz invariant. Many of the proofs I have read use the step function (or ...
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20 views

Experimentally realizable states for bosonic quantum fields

I would like to know which type of quantum states of a bosonic field, that have an explicit analytical expression as vectors/density matrices in a symmetric Fock space, can be prepared in an ...
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15 views

Computation of the partition function of a fermionic oscillator

I don't understand the following steps in the calculation of the partition function for a fermionic oscillator (Nakahara). The eigenvalues of the operator ...
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26 views

Fermionic oscillator and Hurwitz zeta function

Good resources for calculating Partition function of the fermionic oscillator using the Hurwitz zeta function? I liked the way Nakahara explain this, but some parts are really tricky for me (e.g. the ...
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69 views

Quantum Mechanics and Economics… What

I was reading this paper: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2002698&download=yes The author has the model presented here: ...
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54 views

Field states, particles, QFT

I'm trying to self-study QFT and write a presentation paper on neutrinos. Regarding the $\left\{ \nu_L, \nu_R, \bar{\nu}_L, \bar{\nu}_R \right\}$ set of neutrino states, what is the correct word to ...
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55 views

Deriving effective model without integrating out degrees of freedom in path integral formalism?

In path integral formalism of quantum field theory (particle physics or condensed matter), one can in principle integrate out part of the degrees of freedom so as to attain an effective model ...
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1answer
25 views

Why IR divergences cancel by cross sections of next-to-leading diagrams?

I was reading QFT & Standard Model by Schwartz, Chapter 20 which is about IR divergences. He says that IR divergences only cancel cross sections for processes involving different initial or ...
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2answers
48 views

Understanding notation regarding particles states and wavefunctions

In the development in my notes of second quantisation I have a problem in understanding notation. We start by considering a basis $\psi_i(\mathbf{r})$ for the Hilbert space of single particle ...
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45 views

Spinor helicity formalism, exact form of the spinors

I am trying to understand how to perform computations with the spinor helicity formalism, I am studying on this review http://arxiv.org/abs/1308.1697. I have stumbled upon a problem though, in pag. ...
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41 views

Need help understanding Peskin&Schroeder QFT

I don't understand (19.73) in Peskin & Schroeder Introduction to QFT \begin{eqnarray} \sum_n \phi^{\dagger}_n(x) \gamma^5 \phi_n(x) &=& \lim_{M \rightarrow \infty} \sum_n ...
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37 views

Error in setting $m_{proton} = m_{neutron}$

Is the following reasoning correct, I'm doing mostly relativistic calculations so basically all masses come in squares. Suppose I have some expression that contains both the proton and the neutron ...
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39 views

What are the zero point energy densities of the individual quantum fields?

I'm reading through "General Relativity - An Introduction for Physicists", by Hobson, Efstathiou, and Lasenby, and I have a question regarding one of the statements related to the cosmological ...
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1answer
59 views

How to find the number of distinct contraction cases in Wick's Theorem?

Let $\mathcal{G}^8_{un}:=(t_1,t_2,t_1'^3,t_2'^3)=\langle 0 \mid T[Q_{un}(t_1)Q_{un}(t_2)Q(t_1')^3Q(t_2')^3] \mid 0 \rangle_{un}$ We want to use Wicks theorem to write this function as the sum of ...
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36 views

What insights does category theory offer in terms of grand unified theories?

What insights does category theory offer in terms of grand unified theories? Any references to books or papers that give categorical descriptions of any of the common grand unified theories would be ...
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1answer
69 views

Is Elitzur's theorem valid only in lattice field theory?

Elitzur's theorem, stating that spontaneous breakdown of a gauge symmetry is impossible, was originally proved for a lattice gauge theory. Is it valid in continuum field theory? Any ref?
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1answer
38 views

Charge conservation in the complex Klein-Gordon Field

This is an extremely naive question (based on a knowledge of chapter 2 of peskin and schroeder) so apologies for any things that seem obvious. The complex scalar field, when quantized, has a conserved ...
6
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91 views

Why don't we have logarithms or exponentials of the fields in the Lagrangians?

All tbe Lagrangian densities I have seen have always been polynomials of the fields. Is this a coincidence or is there a reason forbid, say, Lagrangians with logarithms or exponentials of the fields?
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1answer
46 views

Photons and EM Fields

I started learning the basic ideas of QFT in an intuitive manner ( withouth any math, only with mental videos and pictures ) some days ago, and i'm finding it completely beautiful [ the idea of ...
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3answers
401 views

What is meant by the term “single particle state”

In a lot of quantum mechanics lecture notes I've read the author introduces the notion of a so-called single-particle state when discussing non-interacting (or weakly interacting) particles, but none ...
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29 views

Scattering Amplitude Not Invariant under Little Group?

I am trying to make sense of scattering amplitude recently. In some literature people say that if some number of massless particles collide together, one can theoretically express the scattering ...
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1answer
38 views

Connections between Density Matrix Renormalization Group and Conformal Field Theory

Can we use the density matrix renormalization group (DMRG) method to understand problems in conformal field theory? I have been trying to find some connections, but nothing is coming up when I search. ...
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1answer
54 views

Where does this hyperbolic tangent in Nakahara's text come from?

I don't see why the term with $\tanh$ appears in the equation 1.164 The textbook is the second edition of Geometry, Topology and Physics
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1answer
69 views

Is $SU(2)$ really broken by the Higgs VEV or just hidden?

It's generally stated in the textbooks that whent the Higgs field acquires a certain vev the corresponding symmetry is spontaneously broken. For example in A. Zee - QFT in a Nutshell: But none of ...
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1answer
45 views

Chiral anomaly in Weyl semimetal

In the presence of electromagnetic fields $E$ and $B$, four current is not conserved in a Weyl semimetal i.e. $\partial_{\mu} j^{\mu}\propto E\cdot B \neq 0$. There are some proofs in the literature ...
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2answers
51 views

Explanation on anticommutation relations

Setup Given two states: $|K\rangle=a_i^+a_j^+|\rangle$ and $|L\rangle=a_k^+a_l^+|\rangle$. Evaluating the overlap: $\langle K|L\rangle=\langle|a_ja_ia_k^+a_l^+|\rangle$ Introducing: ...
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1answer
27 views

Why does trying to remove a non-existing electron from a state give zero?

Setup Creating an electron that is already in a basis set is zero (Pauli's principle): \begin{equation} a_i^+ | \chi_i \cdots \chi_k \cdots \chi_l \rangle = | \chi_i \chi_i \cdots \chi_k \cdots ...
4
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1answer
48 views

Why should Ward identities only be used with the effective action (as opposed to the generating functional for connected diagrams)?

My question is about the derivation of Ward identities. I will sketch it here in the case of an O(N) symmetric model and point out what it bothering me when I am done. I am being very sloppy with the ...
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50 views

Situation after Saini & Stojkovic's paper on unitarity in gravitational collapse and non-formation of black holes?

In their paper, Anshul Saini and Dejan Stojkovic [1] claimed that by calculations it is possible to demonstrate that in a gravitational collapse of a disk, an event horizon is never made for a far ...
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44 views

How many quantum fields are there?

I'm just an aficionado, but my understanding is that in QFT, the photon is an excitation of the electromagnetic field, the electron is an excitation of the electron field, and so on. Is there a ...
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72 views

Phenomena in the intersection of general relativity and quantum mechanics

I am looking for physical phenomena that have aspects involving both general relativity and quantum mechanics. The only example I know is Hawking radiation. While black holes are objects that cannot ...
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17 views

How would I prove the gamma normalization relation without Clifford Algebra? [duplicate]

The equation in question is $$ \left ( \gamma ^{\mu } \right )^{\dagger }=\gamma ^{0}\gamma ^{\mu }\gamma ^{0}$$
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38 views

QFT Calculations via Holographic Duality

Holographic duality tells us that there is a duality between anti-deSitter space and lower dimensional conformal field theory. However, what quantum phenomenon, exactly, can we calculate using the ...
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1answer
59 views

Ground state for interacting field thoeries

Are there references where the ground state of an interacting quantum field theory is explicitly written in terms of states of the underlying free theory? For example, let us suppose to have a self ...
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1answer
51 views

About states, observables and the wave functional interpretation in QFT with gauge fields

First of all, I'm a mathematician, so forgive me for my possible trivial mistakes and poor knowledge of physics. In a QFT, we just start with a field (scalar, vectorial, sponsorial, gauge etc), so I ...
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1answer
32 views

Temperature and Renormalization Scale in QFT

A particle physicist told me that everything in Peskin & Schroder is at zero temperature, and once you consider finite-$T$ QFT, things become more complicated. Meanwhile, I sometimes see people ...
4
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1answer
84 views

How GR, QFT, or string theory address the one-directional feature of time?

It seems to me today's theoretical relativistic physics treat time and space on equal footing, with manifold diffeomorphism structure decoded in metric. However an obvious difference is that time is ...
2
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37 views

Why is it correct to estimate divergences by the cutoff in QFT?

Let's say we have a linear divergence in a quantum field theory. The way to deal with this infinite quantum correction is to go through the whole process of renormalization. However, quite often, ...
2
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1answer
62 views

How do you prove that $L=I-V+1$ in $\lambda\phi^4$ theory?

It is known that the number of loops in $\lambda\phi^4$ theory is given by the formula $$L=I-V+1$$ where $L$ is the number of loops, $I$ the number of internal lines and $V$ the number of vertices. ...
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46 views

Why is the strong CP term $ \theta \frac{g^2}{32 \pi^2} G_{\mu \nu}^a \tilde{G}^{a, \mu \nu}$ never considered for $SU(2)$ or $U(1)$ interactions?

The Lagrangian one would write down naivly for QCD is invariant under CP, which is in agreement with all experiments. Nevertheless, if we add the term \begin{equation} \theta \frac{g^2}{32 \pi^2} ...
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1answer
43 views

How can one prove that there cannot exist a conformal primary, in the case of free field theory, that doesn't saturate the unitarity bound?

In free field theory, the full list of conformal primaries, is given by the Twist-2 operators. These have $\Delta = l+2$, which is also the saturation condition for the unitarity bound for $l \neq 0$. ...
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1answer
299 views

Do electrons oscillate into muons just like electron-neutrinos into muon-neutrinos?

And if not, why? What is the difference to neutrinos oscillations?
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1answer
38 views

What's the phenomenon where it looks like more particles exist at relativistic speeds?

From the perspective of an observer moving close to the speed of light, the surrounding environment has very high energy which leads to pair production. What is the name of this phenomenon? I can't ...
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32 views

Pion decay exercise in Griffiths books

I have questions about pion decay problem. In Griffith "Introduction to Elementary Particles" 1st edition, 1987, question number 10.10 : Analyze $\pi^-$ decay as a scattering process, using the ...
2
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1answer
50 views

Order of Feynman diagrams for electroweak processes?

I want to compare two Feynman diagrams and be able to say which one describes a process that is more likely to happen. As far as I understand, this is done by considering the order of the diagram. ...
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Are there any in depth superfluid mechanic analyses of spacetime?

Has there been much work done that treats particles as vortexes in a fluid, or dark matter as bubbles in this fluid (bending space in the same way massive particles (vortexes) are observed to do, but ...
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35 views

Topological term under electron-electron interaction

By integrating out fermions in gapped Dirac Hamiltonian, one can obtain a topological term for topological insulator. Why there is no further correction to this term when electron-electron interaction ...
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2answers
136 views

Non-relativistic QFT Lagrangian for fermions

Take the ordinary Hamiltonian from non-relativistic quantum mechanics expressed in terms of the fermi fields $\psi(\mathbf{x})$ and $\psi^\dagger(\mathbf{x})$ (as derived, for example, by A. L. Fetter ...
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57 views

using tetrads to glue local currents into global currents

According to John Baez it is possible to take a locally conserved tensor $\nabla_\mu\: T^{\mu\nu}(x)=0\ \ \ \ \ \mbox{(locally)}$ and convert it to a globally conserved tensor by "patching" ...