English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

This is mainly a lecture note taken by myself following Weinberg's book, butalso contains some corrections to the abuse of mathematical treatment. Thisarticle discusses projective unitary representations of Poincare group on thesingle particle space, multi particle space also known as the Fock space,creation and annilation operators, construction of free quantum fields and thegeneral relation between spin of state and spin of field. Both massive andmassless cases are considered. CPT is not considered. The first section brieflyreviews the basics of representation theory. This article further points outsome of the wrong treatment of mathematics in the book of Weinberg, andreformulates them, including: Wigner's classification needs to be pass to theuniversal cover via Bargmann's theorem, there is no projective representationof Poincare group on Fock space in general, the Lorentz transformation offields need to be formulated with representations of the universal covers,Dirac representation is not a linear representation of the Lorentz group. Thisarticle also discusses the physical meaning of the state representation and itsrelation with Schrodinger equation, compare its difference with staterepresentation, and the reason of equations of relativistic quantum mechanicsshould be understood as a field equation rather than a wave function equation.of equations of relativistic quantum mechanics should be understood as a fieldequation rather than a wave function equation.

Representation theory in the construction of free quantum field