Relativistic Hamiltonian Formalism in Quantum Field Theory and Micro-Noncausality

Relativistic Quantum Field Theory

Hamiltonian Formalism in Quantum Mechanics

To Vladimir Igorevich Arnol'd with admiration, on occasion of his 60 th birthday. Abstract Heisenberg motion equations in Quantum mechanics can be put into the Hamilton form. The difference between the commutator and its principal part, the Poisson bracket, can be accounted for exactly. Canonical transformations in Quantum mechanics are not, or at least not what they appear to be; their propert...

Hamiltonian formalism with several variables and quantum field theory: Part I

We discuss in this paper the canonical structure of classical field theory in finite dimensions within the pataplectic hamiltonian formulation, where we put forward the role of Legendre correspondance. We define the Poisson p-brackets and ωbrackets which are the analogues of the Poisson bracket on forms. We formulate the equations of motion of forms in terms of p-brackets and ω-brackets with th...

Quasiparticle excitations in relativistic quantum field theory

We analyze the particle-like excitations arising in relativistic field theories in states different than the vacuum. The basic properties characterizing the quasiparticle propagation are studied using two different complementary methods. First we introduce a frequency-based approach, wherein the quasiparticle properties are deduced from the spectral analysis of the twopoint propagators. Second,...

Unstable Systems in Relativistic Quantum Field Theory

We show how the state of an unstable particle can be defined in terms of stable asymptotic states. This general definition is used to discuss and to solve some old problems connected with the short-time and large-time behaviour of the non-decay amplitude. CERN-TH/97-246 September 1997 ⋆ Address from Sept 1st, 1997 to August 31st, 1998.