From Classical Mechanics to Quantum Field Theory

Index

C∗-algebra, 89
∗

-algebra, 89

-homomorphism, 89

-isomorphism, 89

-representation, 93

admissible triple, 20, 23
analytic vector, 101
atomicity, 135
atomisticity, 135

Banach algebra, 89
Bargmann-Fock
kernel, 34, 35
representation, 6, 33
Bogoliubov, Parasiuk, Hepp and
Zimmerman, 228
Boolean algebra, 129
bosons, 44, 46

Casimir effect, 192, 209, 210, 230
Cauchy
conditions, 194
data, 234
central extension, 164
coherent states, 28–31
generalized, 36, 39
of bosonic type, 37
of fermionic type, 38
path integral, 45

commutant, 147

commutation relations, 11, 49, 53, 54

canonical, 5, 10, 37, 38, 79

Weyl, 51

complex structure, 20, 23

composite systems, 13, 77

conformal

group, 224

invariant, 229

invariant theories, 223

symmetry, 224

transformations, 223

constant of motion, 169

covering property, 135

deficiency indices, 100

Dirac, 190, 192

equation, 199

Dirichlet boundary conditions, 230

displacement operator , 29, 32

dynamical symmetry, 169

Euclidean

approach, 220

classical action, 225

covariance principles, 226

field operators, 221

functional integral, 234

invariance, 222

principles, 222

propagator, 234

239