1
vote
1answer
159 views

Grassmann fields according to Peskin and Schroeder

On page 301 in Peskin and Schroeder, they claim that a Grassman field $\psi(x)$ may be decomposed as $$\psi(x) = \sum_i c_i \phi_i(x),$$ where the $c_i$ are Grassmann numbers and the $\phi_i$ are ...
5
votes
1answer
253 views

Grassmann Variables Representation?

It might be a silly question, but I was never mathematically introduced to the topic. Is there a representation for Grassmann Variables using real field. For example, gamma matrices have a ...
4
votes
2answers
278 views

Combinatorial sum in a problem with a Fermi gas

I'm solving a problem involving a Fermi gas. There is a specific sum I cannot figure my way around. A set of equidistant levels, indexed by $m=0,1,2 \ldots$, is populated by spinless fermions with ...
11
votes
3answers
1k views

What are the mathematical problems in introducing Spin 3/2 fermions?

Can the physics complications of introducing spin 3/2 Rarita-Schwinger matter be put in geometric (or other) terms readily accessible to a mathematician?
2
votes
1answer
324 views

What are Grassmann (even/odd) numbers used in superalgebras?

Are Grassmann numbers a concept of graded Lie algebras or is something specific to superalgebras? What are they (i.e: how are they defined, important properties, etc.)? Is there a reasonable ...