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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Mathematical Prerequisites for QFT [closed]

I am curious about which areas of mathematics one should be comfortable with before learning QFT. I am familiar with the "learn-it-as-you-go" approach often advocated in physics, but would like to ...
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60 views

Ambiguous points in spontaneous symmetry breaking of discrete symmetry

For a discrete symmetry: At the minimum value of the potential, $V$, in the Lagrangian density, why do we take $\phi= \langle v\rangle + \eta$? Aren't we deliberately breaking the symmetry? If we ...
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1answer
100 views

How does string theory describe classical gravity theory, and QFT? [closed]

I am learning string theory, as I understand, gravitons exist as modes in string excitations, and also other particles. It gave me this picture: a lot of strings fulling in the spacetime, excitations ...
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2answers
88 views

Is it possible to create matter from space?

Like could maybe fluctuate the space some how and make the virtual paricles turn into normal matter
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58 views

What's the value of the coupling constant in interacting field theories?

Consider this Lagrangian : $L = \frac{1}{2}(\partial_\mu \Phi)^2 - \frac{M^2}{2}\Phi^2 +\frac{1}{2}(\partial_\mu \phi)^2 -\frac{m^2}{2} \phi^2 -\mu\Phi\phi^2$ Its interaction term is given by : ...
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89 views

Moduli spaces in string theory vs. soliton theory

In both string theory and soliton theory, moduli spaces are frequently used. As far as I known, for soliton theory, moduli spaces are something like collective coordinates for solitons, and for ...
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1answer
64 views

Difference between Veneziano amplitude and Virasoro shapiro amplitude

I have been study about Veneziano amplitude and Virasoro Shapiro amplitude. I want to summarize this two amplitude in the following way, please check that i am understand them properly. Veneziano ...
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1answer
74 views

change of variable in a 2-loop integral

given the 2 loop integral $$ \int dq_{1} \int dq_{2}F(q1,q2) $$ (1) then in dimension D=4 our integral will be a 8-dimensional integral so why can not make a change of variable to 8-dimensional ...
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2answers
117 views

Does one really need classical physics in order to understand quantum physics? [closed]

I want to start studying quantum mechanics, and then move to quantum field theory. I have a strong mathematical background, and I think this aspect of quantum physics won't be a problem to me. Though, ...
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111 views

Lorentz symmetry and Noether's theorem

I'm trying to overcome some misunderstanding that I have in Noether's theorem. There is formula in David Gross's Lectures on QFT for Noether's theorem: ...
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1answer
125 views

In QFT, why do fermions have to anticommute in order to insure causality?

I have seen this question and I believe I understand the answer to it. However, AFAIK, only for bosons the causality condition is a vanishing commutator. For fermions we expect the anticommutator ...
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123 views

LHC data and mathematics of QFT

I'm reading Frederic's Paugam Towards the Mathematics of Quantum Field Theory, an advanced theoretical physics book. I would like to know how I could apply the theories in this book. For example, ...
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84 views

Converting two component product to four component notation

Consider the product of two left Weyl spinors in the notation commonly found in supersymmetry, \begin{equation} \chi ^\alpha\eta_\alpha = \chi ^\alpha \epsilon _{ \alpha \beta } \eta ^\beta ...
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An electron is an excitation of the electron field. So when we observe a higgs boson that means we've excited the higgs field?

See this related question: If particles are excitations what are their fields? I ask this question because, according to a lecture, the higgs boson was frozen into a "matrix" at some point before ...
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211 views

Fundamental representation in quantum field theory

In QFT we associate to each Gauge theory a continuous group of local transformations (a Gauge group), and then we require\define fermion fields to be irreducible representations belonging to the ...
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71 views

Understanding the effective low-energy Lagrangian for hadrons

My course in Higgs Physics is discussing a two-nucleon low-energy effective theory of hadron interaction. With $\psi=(p,n)$, the pion is defined as $\vec{\pi}= i \bar{\psi}\vec{\tau} \gamma_5 ...
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80 views

What is the reason for the $ i \tau_2 $ - factor in the higgs coupling with up-type quarks?

The quark mass term in the Standard Model Lagrangian looks like this: $$ L = - \lambda_d \bar{Q}\phi d_R - \lambda_u \bar{Q} i \tau_2 \phi^* u_R $$ What is the reason for the $ i \tau_2 $ - ...
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58 views

Why does the state space contain states with negative norm and what would be an example?

My lecture script of Quantum Field Theory states that " the state space contains states with negative norm ". Why does it have to be like this and what would be an example fo such a state?
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286 views

For a particle to have physical mass, is it always necessary to have a mass term in the lagrangian?

Since the self-energy adds to the bare mass defined in the Lagrangian, is it possible to create a physical particle mass from the self-energy alone, with no mass terms occuring in the Lagrangian? On ...
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1answer
100 views

Why doesn't the photon have mass? The Higgs mechanism and pre-electroweak epoch

1) When electroweak separation occurred, 'why' wasn't the photon 'given' mass like the W and Z bosons? i.e why don't photos interact with the higg's field? 2a) How well is the higg's mechanism ...
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1answer
64 views

Scalar Particles, Flavor Changing Processes and Gauge Symmetries

Let's consider an extended version of the Standard Model (SM) with a new Yukawa operator of the form $$ \sum_\ell g_\ell\bar{\ell}\ell \phi ,$$ where $\ell$ is any lepton of the SM and $\phi$ is a new ...
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1answer
130 views

Vacuum stability in quantum field theory

What exactly do people mean when they talk about the scale dependence of the effective potential ($V$)? I explain the motivation for my question (and hence my confusion) below. Please correct me as ...
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1answer
97 views

Group theoretic way to find charges after SSB

I was wondering what is the group theoretic way to find the resulting charges of matter fields after a scalar field is given a vev. In the case of the EW symmetry breaking, one can directly read the ...
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2answers
88 views

Gross-Neveu model analytic solution [closed]

I need to find an analytic solution via asymptotic expansion for the following system of equations: \begin{align} & i(u_t+u_x) + v = 0 \\ & i(v_t-v_x) + u = 0 \end{align} \begin{equation} ...
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143 views

Eigenstates of a Hermitian field operator

Consider a Hermitian field operator $\phi(x)$ with eigenstates satisfying $$ \phi(x) |\alpha\rangle = \alpha(x) | \alpha \rangle $$ I'm trying to determine the inner product between the eigenstates. ...
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1answer
73 views

A Variation on Laplace's equation (context: Yang-Mills N-Instantons, Rajaraman's book)

Statement of the problem I need to solve the equation \begin{align} 0 = \frac{1}{\phi} \partial_{\sigma}\partial_{\sigma} \phi \hspace{20mm} (1) \end{align} where $\phi$ is a scalar field and ...
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21 views

Problem books like I.E. Irodov for advanced physics [duplicate]

I really enjoyed doing problems from Irodov while learning introductory physics. But I am not able to find a book like that for Graduate level physics. Can you suggest me a book which has good (and ...
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39 views

Using local U(1) Transformation to solve Problem in Path Integral [duplicate]

When we develop photon path integral, we assume that the current is always conserved. But if we consider interaction between electron/positron and photon, the Noether current is conserved only when ...
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2answers
88 views

Is negative mass for a bound system of two particles forbidden?

Is there any theorem that forbids the bound system of two massive particles to have negative mass?
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64 views

Hamiltonian Operator for nonrenormalizable Effective Field Theories?

Assuming we have a Effective Field Theory, for example a Real Scalar Field Theory, defined through a Lagrangian density of the form $\mathcal{L}_{eff} = \frac{1}{2}\partial_\mu\phi \partial^\mu\phi - ...
3
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1answer
127 views

Graph Theory and Feynman Integrals

In Vladimir A. Smirnov's book Analytic Tools for Feynman Integrals, Section 2.3, the alpha representation of general Feynman integral takes the form $$ F_{\Gamma}(q_1,\ldots,q_n;d) = ...
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1answer
237 views

Is the Higgs Boson a Force Carrier? [duplicate]

I am told there are four fundamental forces, and each of these forces has a boson that acts as its carrier. Reading this http://www.fnal.gov/pub/science/inquiring/questions/higgs_boson.html I find ...
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Propagators, path Integrals, transition amplitudes, Green's functions etc

I'm trying to make a simple conceptual map regarding some of the things in the title as they pertain to quantum mechanics and or quantum field theory, and I'm finding that I'm a little perplexed about ...
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2answers
218 views

Quantum Yang-Mills Theory and AdS/CFT

I just read the first chapter of Becker-Becker-Schwarz. To quote: A remarkable discovery made in the late 1990s is the exact equivalence (or duality) of conformally invariant quantum field ...
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3answers
426 views

Why is normal ordering a valid operation?

Why is normal ordering even a valid operation in the first place? I mean it can give us some nice results, but why can we do the ordering for the operators like that? Is its definition motivated by ...
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1answer
65 views

What is the P-parity, T-parity and C-parity of graviton? Are these conserved in general curved space-time?

I'm curious about the P,T,C-parity of graviton? 1)Are these graviton's parities even or odd? 2)Is the C,P,T-parity alternatively conserved in Einstein gravity? And does the CPT theorem still hold ...
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1answer
93 views

Operator product expansion in CFT

I'm on Polchinski's p39. Can someone please tell me the steps in the equivalence below? $$\exp\left[\frac{\alpha'}4\int d^2z_4 d^2z_5\ln|z_5-z_4|^2\frac{\delta}{\delta X^\mu(z_4,\bar ...
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1answer
139 views

Quantum field theory: field operators in terms of creation/annihilation operators

I am learning Quantum Field Theory and there is a step in my notes that I do not really understand. It starts with the classical definitions of position $q$ and momentum $p$: $$ q = ...
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66 views

Why is the Higgs mass renormalization considered a fine-tuning problem, while the electron mass (in QED) isn't?

Don't both masses require infinite corrections in their renormalization procedure? It is my understanding that the electron self-energy in QED increases to infinity with increasing cutoff value on ...
5
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1answer
129 views

Why do people look for a field formalism for String Theory

String theory was originally formulated from a perturbative description (using quantum mechanics (QM) and replacing points by strings and evaluating path integral). Still, although QM has an upgrade ...
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105 views

General definition of vector spinor and spin

I am looking for basic and exact definitions of fundamental physical consepts in graduate level. I reach this following definitions. Could you please help to improve these definitions. Spin: ...
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1answer
74 views

Hermiticity of the quantum field

The quantum field resultant from the quantization of a real classical field is hermitian, but why the quantum field corresponding to a complex classical field should be non-hermitian?
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3answers
156 views

How do charged particles interact?

You'll have to forgive me if this question is too wrapped up in "classical" thinking. I've read that electrons and protons interact by trading photons, but this only raises more questions. What ...
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35 views

Joint probability function for the values of a free field at two different points

For a free real field $\phi$ in its ground state, is there a way to find the probability distribution $p(\phi_x,\phi_y)$ for joint measurement of $\phi(x)$ and $\phi(y)$ at two spacelike-separated ...
15
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1answer
292 views

Origin of phases in amplitudes in QFT

Amplitudes in QFT are typically real. I'd like to understand the physical meaning of an amplitude having a phase. I know of three ways that amplitudes can get a phase: If the couplings have an ...
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171 views

Is the harmonic oscillator potential unique in having equally spaced discrete energy levels?

I was wondering if the good old quadratic potential was the only potential with equally spaced eigenvalues. Obviously you can construct others, such as a potential that is infinite in some places and ...
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98 views

The relationship between angular and linear momentum

Why is orbital angular momentum not 0 when spin and linear momentum are not collinear? Why can it be 0 when spin and linear momentum are parallel? Like in the example of a scalar field at rest ...
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1-particle momentum eigenfunction in terms of field operator for real Klein-Gordon field

Suppose $\phi(x)$ is a real Klein-Gordon field, then the single-particle wave function $\psi(x)$ corresponding to a momentum $p$ is given by (QFT, Ryder) $$\psi_p(x)=\langle0|\phi(x)|p\rangle.$$ The ...
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71 views

Is there any difference between massless Dirac fermions and Weyl fermions?

In graphene we call the low energy excitations around the Dirac point Dirac fermions, which are massless. Is this just by convention or is there any further differences between massless Dirac ...