Tagged Questions
1
vote
1answer
50 views
Lie algebra of lorentz group
I'm stuck in following calcualtion from sredniki's QFT book.(Its actually in the solution manual)
How can i get from
$$\delta\omega_{\rho\sigma}(g^{\sigma\mu}M^{\rho\nu} - g^{\rho\nu}M^{\mu\sigma})
...
4
votes
2answers
257 views
Definition of Casimir operator and its properties
I'm not sure which is the exact definition of a Casimir operator.
In some texts it is defined as the product of generators of the form:
$$X^2=\sum X_iX^i$$
But in other parts it is defined as an ...
3
votes
1answer
92 views
Different representations of the Lorentz algebra
I've found many definitions of Lorentz generators that satisfy the Lorentz algebra: ...
9
votes
4answers
359 views
Trace and adjoint representation of $SU(N)$
In the adjoint representation of $SU(N)$, the generators $t^a_G$ are chosen as
$$ (t^a_G)_{bc}=-if^{abc} $$
The following identity can be found in Taizo Muta's book "Foundations of Quantum ...
2
votes
1answer
150 views
Dirac trace theorem
I am unable to prove exactly one trace identity that appears in the appendix of Peskin and Schroeder's QFT book. Can someone help me?
The theorem [Appendix A.4 eqn (A.28)] says that the order of ...
6
votes
1answer
147 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, ...
2
votes
1answer
99 views
Taylor series for unitary operator in Weinberg
On page 54 of Weinberg's QFT I, he says that an element $T(\theta)$ of a connected Lie group can be represented by a unitary operator $U(T(\theta))$ acting on the physical Hilbert space. Near the ...
2
votes
0answers
109 views
Derivation of the enhancement of U(1)$_L$ x U(1)$_R$ to SU(2)$_L$ x SU(2)$_R$ at the self-dual radius
Towards the end of the paragraph with the title String theory's added value 2: enhanced non-Abelian symmetries at self-dual radii and abstract C with current algebras of this article, it is explained ...
2
votes
1answer
71 views
Charge of a field under the action of a group
What does it mean for a field (say, $\phi$) to have a charge (say, $Q$) under the action of a group (say, $U(1)$)?
3
votes
1answer
155 views
Question about the parity of the ghost number operator in BRST quantization
Given a Lie algebra $[K_i,K_j]=f_{ij}^k K_k$, and ghost fields satisfying the anticommutation relations $\{c^i,b_j\}=\delta_j^i$, the ghost number operator is then $U=c^ib_i$ (duplicate indices are ...
