Questions tagged [poincare-symmetry]
The poincare-symmetry tag has no usage guidance.
0
votes
0answers
47 views
Generators of the Poincaré group
I am specifically interested in constructing the generators of an Poincaré group for a 2+1 dimensional Euclidean field theory. But I am pretty new to the subject, so I would like to ask some basic ...
0
votes
0answers
52 views
Representation of Poincaré group
Let's consider the most general Lorentz transformation: $x'^{\mu} = \Lambda^{\mu}_{\ \ \nu} x^{\nu} + a^{\mu}$. These transformations form the Poincaré group. The generators of translations of this ...
0
votes
1answer
52 views
Doubt in the Poincaré algebra and one-particle states
I am studyng the algebra of Poincaré group and the definition of one particle states using the Weinberg book "Quantum theory of Fields" (vol. 1), but I'm having a hard time understanding part of the ...
0
votes
1answer
67 views
Reference request for Lie algebras
My future adviser just published a beautiful paper, https://arxiv.org/abs/1904.08304, and I am looking for some references/textbooks to look into the following concepts:
Lie algebra (central) ...
2
votes
1answer
75 views
Relativistic quantum mechanics ${}$
I am reading Weinberg's book "Quantum theory of field".
Сould you explain to me the following things? Vol.1, page 60:
How are we equating the coefficients? How we find the formula (2.4.8)?
2.3.10: ...
0
votes
0answers
39 views
Massive chiral fermions
The main question is: why does nobody care about massive chiral fermions?
It is well-known that in QFT (in the axiomatic framework of Garding & Wightman) the quantum field transform according (...
2
votes
0answers
46 views
Understanding the idea behind the super-Poincaré algebra
On the Super-poincaré algebra wiki page (https://en.m.wikipedia.org/wiki/Super-Poincaré_algebra), it says:
"If Minkowski space-time belongs to the adjoint representation, then can Poincaré symmetry ...
0
votes
2answers
43 views
Is the antisymmetrisation of $a^{\mu}b^{\nu}\epsilon_{\mu\nu}= a^{[\mu}b^{\nu]}\epsilon_{\mu\nu}$ with antisymmetric tensor $\epsilon$ mandatory?
When in tensor algebra the product of 2 vectors with a antisymmetric tensor appear, is antisymmetrisation compulsory ? Given an antisymmetric tensor $\epsilon_{\mu\nu}$, is
$$a^{\mu}b^{\nu}\epsilon_{...
2
votes
0answers
31 views
How is deSitter group tranformations different from poincare group transformations
In QFT, we have studies Poincare group of massive and massless particles. Is the deSitter group also useful to study such things? What exactly is the main role of this group in QFT?
I just know the ...
0
votes
0answers
36 views
Check that the Poincaré's transformations form a group structure
How can I answer to this question ? I know that this is a Lorentz transformation + a translation but I don't know how to start. What's the difference between group/group structure ?
3
votes
0answers
51 views
How is Inönü-wigner contraction done?
I have read that little group for the massive particles is $SO(3)$ and for the massless particles is $E(2)$ in 4 dimensions. How does one take zero mass limits for the representations and show that it ...
5
votes
2answers
312 views
Poincare transformations and “three kinds of infinitesimal variations”
I'm currently reading these$^1$ lec. notes as an introduction to relativistic QFT. In chapter two (pp.57-61) he introduces the concept of field variations along with some formulas for the different ...
2
votes
0answers
50 views
Poincaré invariance of linearly polarised plane wave
I am reading a book that just quotes the Lie group generators and the discrete subgroups that leave a linearly polarised plane wave unchanged. And I have no idea how to derive them.
Context
The ...
3
votes
1answer
81 views
Doubts on representations of poincare group and QFT
I am studying Poincare group and encountered the term massless representations of the Poincare group. I know Poincare group is studied by the studying the little group of various momenta, massless and ...
2
votes
3answers
125 views
Lorentz transformation of vector field
Under a Lorentz transformation, a vector field transforms as: $A'_{\mu}(x')=\Lambda^{\nu}_{\mu}A_{\nu}(x)$
My question is, why is the Lorentz transformed vector field evaluated at $x'=\Lambda x$, ...
1
vote
1answer
62 views
Poincare group and free theories
How exactly is the Poincare group related to the free relativistic theories in quantum field theory? I know Poincare group is the Lorentz group along with translations but don't see any connected why ...
0
votes
0answers
51 views
Variation of vector field under Lorentz transformation and gauge transformation
In a paper I am reading, it is stated that under a Lorentz transformation, the coordinates transform as $x^{\mu} \to \Lambda^{\mu}_{\nu}x^{\nu}$, and so the change in the (vector) field at the same ...
2
votes
0answers
55 views
Derivatives in Poincare' gauge theory
I have been reading the lectures: http://www.damtp.cam.ac.uk/research/gr/members/gibbons/gwgPartIII_Supergravity.pdf about Poincare' gauge theory. The Poincare' group is considered as semidirect ...
0
votes
0answers
51 views
How to write the Poincare transformation for an arbitary path in Minkowski space?
So lets Say for arguments sake we have some vector $V^{a}$ and we drag it along some path $\gamma_{1}$ in Minkowski space $R^{3,1}$. For a straight path (represented by a vector $\Delta\overrightarrow{...
1
vote
1answer
73 views
Poincaré and Galilei group - notation
On this slide
it just says that $\mathcal{P}$ and $\mathcal{G}$ are the Poincoré and Galilei groups, but I do not understand what they are made of.
What does $\mathbb{R}^{1,3}$ mean?
Why does $\...
2
votes
1answer
104 views
Doubt in Weinberg's book on Quantum Field Theory
In page number 59 of his book on QFT, Weinberg mentions that for the operator $U$, defined for infinitesimal parameters $\omega$ and $\epsilon$ as:
\begin{equation}
U(1+\omega,\epsilon)=1+\dfrac{1}{2}...
2
votes
1answer
103 views
What sort of particles corresponds to the $(1,1/2)$ representation of the Lorentz group?
Every irreducible massive unitary representation of the Poincaré group is specified by a mass and a non-negative half integer spin. Every massless irreducible unitary representation of the Poincaré ...
2
votes
0answers
90 views
Gravity from algebra
Can someone provide me a reference that describes the gauging of the Poincare algebra to obtain Einstein's relativity?
"It is well known that Einstein’s formulation of gravity can be obtained by ...
5
votes
2answers
131 views
GR as a gauge theory: there's a Lorentz-valued spin connection, but what about a translation-valued connection?
Given an internal symmetry group, we gauge it by promoting the exterior derivative to its covariant version:
$$
D = d+A,
$$
where $A=A^a T_a$ is a Lie algebra valued one-form known as the connection ...
0
votes
0answers
8 views
Fractal discrete networks approximations and Poincaré invariance?
In the link below one may find interesting paper by Sabine Hossenfelder, about finite networks symmetry due to Poincaré group. According to this thesis locally finite networks cannot be Poincaré ...
1
vote
1answer
102 views
Physical meaning of the Casimir operators of Poincarè algebra
If one considers the algebra $su(2)$, it is well known that the Casimir Operator is
$$
C=L_1^2+L_2^2+L_3^2.
$$
It corresponds to the total angular momentum and correctly is a conserved quantity.
...
2
votes
1answer
143 views
What about the (1, 1/2), or (3/2, 1/2) representations of the Lorentz group?
All irreducible finite dimensional complex representations of the Lorentz group can be specified by two positive half-integers, i.e. $(j_1, j_2)$. The $(0,0)$ representation is the trivial scalar ...
1
vote
2answers
155 views
Why do we want supersymmetry transformations to form a group?
I am getting introduced into supersymmetry reading Ryder "Quantum Field Theory". I have taken an introductory course on QFT last semester so I am far from being an expert. Sorry if this is a silly ...
3
votes
1answer
128 views
Is there a type of supersymmetry where supercharges have spin 3/2?
Thinking of supersymmetry operators $Q$, they mix fields with a certain spin with fields with spin $1/2$ higher or lower.
Thinking of open bosonic strings from string theory, the different modes are ...
3
votes
1answer
96 views
Why do we require that all fields are scalars under spacetime translations?
In his book A Modern Introduction to Quantum Field Theory, Michele Maggiore affirms that
We require that all fields, independently of their transformation properties under the Lorentz group, behave ...
1
vote
0answers
60 views
More than one Poincare-invariant vacuum in case of spontaneous symmetry breaking?
It is said in axiomatic quantum field theory approach that Poincare-invariant vacuum is unique. However, in case of spontaneous symmetry breaking - such as Mexican hat example - it seems that more ...
3
votes
1answer
145 views
Wigner Classification via the orbit structure of the Lorentz group
I have been reading and writing a lot about the Wigner Classification of irreducible unitaries of (the universal cover of) the Poincaré group lately, both from a physicist's and a mathematician's ...
3
votes
1answer
111 views
Does Haag's theorem say covariant transformation of interacting field is not possible?
In https://www.physicsforums.com/threads/haags-theorem-perturbation-existence-and-qft.177865/#post-1384425 #2 post by meopemuk (Eugene) say that Haag's theorem says:
$$U(\Lambda)\Phi(x) U^{-1}(\...
8
votes
0answers
131 views
Can cut-off regularisation cause a Poincaré anomaly?
Momentum cut-off regularisation leads to non-covariant results, i.e., it breaks the Poincaré covariance of the theory. Is there any guarantee that Poincaré covariance is always restored when we remove ...
asked Apr 27 '18 at 18:50
AccidentalFourierTransform
26k14 gold badges73 silver badges131 bronze badges
1
vote
0answers
127 views
What is the mathematical formulation of the universality of physics in spacetime?
Consider a general spacetime manifold $\mathcal{M}$ of a given dimension (usually $D = 4$). I call two physical constraints that should be imposed on any reasonable classical theory of physics :
...
3
votes
0answers
39 views
Is there any feature which distinguishes the Hamiltonian in the Poincare algebra?
The Poincare algebra is defined as
\begin{align*}
i[J^{\mu\nu},J^{\rho\sigma}]&=\eta^{\nu\rho}J^{\mu\sigma}-\eta^{\mu\rho}J^{\nu\sigma}+\eta^{\sigma\nu}J^{\rho\mu}-\eta^{\sigma\mu}J^{\rho\nu}\\
...
7
votes
1answer
511 views
Is local Lorentz + diffeomorphism invariance equivalent to full local Poincaré invariance?
Consider classical General Relativity without the torsion field (the affine connection is already assumed to be symmetric from the start). It is well known that this theory is independent of the ...
7
votes
1answer
278 views
Why aren't infinite-dimensional representations of the Poincaré group classified by *two* half-integers?
It is known that to specify a finite-dimensional irreducible representation of the Lorentz group, one needs to specify two half-integers, $(j_1,j_2)$. For instance, the left-handed and right-handed ...
2
votes
1answer
86 views
Is the Rindler vacuum invariant under Poincare symmetries?
More generally, when we quantize fields in the Rindler space and obtain the Fock space of Rindler particles - does that carry a unitary representation of the Poincare symmetries? It should not, ...
1
vote
2answers
632 views
Casimir Operators and the Poincare Group
Following along in QFT (Kaku) he introduces the Casimir Operators (Momentum squared and Pauli-Lubanski) and claims that the eigenvalues of the operators characterize the irreducible representations of ...
2
votes
1answer
187 views
Does $[P_j,B_k]=i(Mc^2)\delta_{jk}$ imply particle number conservation?
From reading Weinberg's Quantum Theory of Fields, Vol. 1, I learnt that for the Galilean group $[P_j,B_k]=i(Mc^2)\delta_{jk}$, and for the Poincare group $[P_j,B_k]=iH\delta_{jk}$ where $P_j$ and $B_k$...
0
votes
1answer
92 views
Definition of particles in Schwartz, Quantum field theory and the standard model
I would like to check if my understanding of the definition of a particle is right. I also have some questions on things I still don't understand.
On pages 109-111 of Schwartz, Quantum field theory ...
11
votes
1answer
330 views
Can Poincare representations be embedded in non-standard Lorentz representations?
My impression for how Poincare and Lorentz representations are linked in $3+1$ dimensions is:
Assuming positive mass for simplicity, irreducible representations of the Poincare group are indexed by ...
2
votes
0answers
79 views
Is there any non-trivial sense in which the spacetime symmetries in the SM gauge QFT are made local?
I know there is a trivial sense in which they are made local by tensoring them with the internal local gauge symmetries through a direct product as per Coleman-Mandula theorem, but it bothers me a bit ...
1
vote
0answers
12 views
Massive axial field interacting with massive fermions: number of independent components
Assume a model of massive fermion $f$ interacting with an axial boson $A_{\mu}$:
$$
\mathcal{L} = -\frac{1}{4}A_{\mu\nu}A^{\mu\nu}+\bar{f}i\gamma_{\mu}\partial^{\mu}f+\bar{f}\gamma_{5}\gamma_{\mu}f A^{...
4
votes
2answers
232 views
How are the two independent states of polarization of photon related to the two helicity states?
(1) In the canonical quantization of the free electromagnetic field, the Coulomb gauge condition $$A^0=0,~~ \nabla\cdot\textbf{A}=0\tag{1}$$ implies that the polarization vector $\epsilon^\mu$ ...
2
votes
0answers
65 views
SUSY: No-Go theorems?
According to the Coleman-Mandula theorem, there is no trivial unification or the Poincaré symmetry and the internal gauge symmetries. However, if we give up the commutator bounds, and we allow for ...
1
vote
1answer
208 views
0
votes
1answer
159 views
Lorentz Transformations And Space-time origins
When we restrict our attention to homogeneous Lorentz Transformations, we restrict two observers to have the same space time origin. Yet they could be moving w.r.t each other with a constant velocity. ...
4
votes
1answer
712 views
Difference between dynamical and geometric phase
How can one differentiate between dynamical and geometric phase produced in the time dependent Schrodinger evolution of a quantum system? How we can describe or define these two terms separately?
