Functional representation for fermionic quantum fields

Journal Article · Fri Apr 15 00:00:00 EDT 1988 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.37.2206· OSTI ID:5375373

Floreanini, R; Jackiw, R

A functional representation for fermionic quantum fields is developed in analogy to familiar results for bosonic fields. The infinite Clifford algebra of the field anticommutator is realized reducibly on a Grassmann functional space. On this space, transformation groups may be represented without normal ordering with respect to a Fock vacuum, and a projective representation for the two-dimensional conformal group is found, which is compared to the corresponding representation in terms of bosonic fields. When a quadratic Hamiltonian for the Fermi fields is posited, a Fock space can be constructed after a prescription for filling the Dirac sea is selected. Different filling prescriptions lead to inequivalent Fock spaces within the functional space. Explicit eigenfunctionals exhibit the peculiarities of fermionic field theory, such as fractional charge, Berry's phase, and anomalies.

• Research Organization: Center for Theoretical Physics, Laboratory for Nuclear Science Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
• OSTI ID: 5375373
• Journal Information: Phys. Rev. D; (United States), Vol. 37:8
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
QUANTUM FIELD THEORY
FUNCTIONAL ANALYSIS
BOSONS
EIGENFUNCTIONS
EIGENSTATES
FERMIONS
HAMILTONIANS
QUANTUM MECHANICS
RENORMALIZATION
TWO-DIMENSIONAL CALCULATIONS
WAVE FUNCTIONS
FIELD THEORIES
FUNCTIONS
MATHEMATICAL OPERATORS
MATHEMATICS
MECHANICS
QUANTUM OPERATORS
645400* - High Energy Physics- Field Theory