The state vector evolution in the interaction of initial measured pure state with collective quantum system or the field with a very large number of degrees of freedom N is analysed in a nonperturbative QED formalism. As the example the measurement of the electron final state scattered on nucleus or neutrino is considered.In the nonperturbative field theory the complete manifold of the system states is nonseparable i.e. is described by tensor product of infinitely many independent Hilbert spaces. The interaction of this system with the measured state can result in the final states which belong to different Hilbert spaces which corresponds to different values of some classical observables,i.e. spontaneous symmetry breaking occurs. Interference terms (IT) between such states in the measurement of any Hermitian observable are infinitely small and due to it the final pure states can't be distinguished from the mixed ones, characteristic for the state collapse. The evolution from initial to final system state is nonunitary and become formally irreversible in the limit of infinite time. The electromagnetic (e-m) bremmstrahlung produced in the electron scattering process contain the unrestricted number of soft photons which radiation flux become classic observable. Analoguous processes which occurs in the second kind phase transitions in ferromagnetic and phonon excitations in cristall lattice are considered briefly.
The state vector evolution in the interaction of initial measured pure state with collective quantum system or the field with a very large number of degrees of freedom N is analysed in a nonperturbative QED formalism. As the example the measurement of the electron final state scattered on nucleus or neutrino is considered.In the nonperturbative field theory the complete manifold of the system states is nonseparable i.e. is described by tensor product of infinitely many independent Hilbert spaces. The interaction of this system with the measured state can result in the final states which belong to different Hilbert spaces which corresponds to different values of some classical observables,i.e. spontaneous symmetry breaking occurs. Interference terms (IT) between such states in the measurement of any Hermitian observable are infinitely small and due to it the final pure states can't be distinguished from the mixed ones, characteristic for the state collapse. The evolution from initial to final system state is nonunitary and become formally irreversible in the limit of infinite time. The electromagnetic (e-m) bremmstrahlung produced in the electron scattering process contain the unrestricted number of soft photons which radiation flux become classic observable. Analoguous processes which occurs in the second kind phase transitions in ferromagnetic and phonon excitations in cristall lattice are considered briefly.
The quantum measurement problem considered for measuring system (MS) model which consist of measured state S (particle), detector D and information processing device O. For spin chains and other O models the state evolution for MS observables measurements studied. It's shown that specific O states structure forbids the measurement of MS interference terms which discriminate pure and mixed S states. It results in the reduction MS Hilbert space to O representation in which MS evolution is irreversible, which in operational formalism corresponds to S state collapse. In radiation decoherence O model Glauber restrictions on QED field observables results in analogous irreversible MS + field evolution. The results interpretation in Quantum Information framework and Rovelli Relational Quantum Mechanics discussed.
The quantum measurement problem considered for measuring system (MS) consist of measured state S (particle), detector D and information processing device (observer) O. It's shown that O states selfreference structure results in principal nonobservability of MS interference terms which discriminate pure and mixed S states. Such observables restriction permit to construct for MS states subjective representation (SR) which describes probabilistic evolution for measurement events observed by O and his subjective information about S values. SR is dual and nonequivalent to MS Hilbert space H for external observer O′. Due to it SR evolution is compatible with Schrodinger linear MS evolution observed by O′. It's argued that SR evolution corresponds to S state collapse for individual events observed by O.
The time irreversible evolution of quantum systems with infinite number of particles (QSINP) was studied within a newly constructed algebraic framework. The QSINP could be described by the quantum infinite lattice field. The *-Algebra R is the set of all dynamic variables of the QSINP, in which a special addition and multiplication operations were defined. The full pure state vector (FPSV) ρ, the pure state vector {ρ_f} and the equivalent relations within them are also well defined. The set of all pure state vectors, which are equivalent to the FPSV ρ, is a Hilbert Space {H_ρ}, if the addition, the inner product and the norm were defined in it. The set of all linear transformation {N_ρ} on {H_ρ} is isomorphic to R, and {{N_ρ},{H_ρ}} is the representation of R, associated with ρ. The *-Algebra R has infinitely many non-equivalent irreducible GNS constructions (representations), associated with different nonequivalent FPSVs respectively. It is proved that, the dynamical motions of the QSINP is totally within the GNS construction associated with the initial pure state vector; However, the time reversal transformation makes the initial FPSV and its corresponding dynamical evolution into another non-equivalent GNS construction. Therefore, within the GNS construction associated with the FPSV, the dynamics of the QSINP is time irreversible. Finally, due to the Liouville operator has real continuous spectrum within the GNS construction, the longtime asymptotic solution of Liouville equation in the GNS construction could be treated by the formal scattering theory. The Master equation with dissipative term was obtained, which is formally irrelevant of the initial state and the corresponding GNS construction. This master equation could be regarded as the evolution equation of the QSINP on R.
The processes of radiation damping and decoherence in Quantum Electrodynamics are studied from an open system's point of view. Employing functional techniques of field theory, the degrees of freedom of the radiation field are eliminated to obtain the influence phase functional which describes the reduced dynamics of the matter variables. The general theory is applied to the dynamics of a single electron in the radiation field. From a study of the wave packet dynamics a quantitative measure for the degree of decoherence, the decoherence function, is deduced. The latter is shown to describe the emergence of decoherence through the emission of bremsstrahlung caused by the relative motion of interfering wave packets. It is argued that this mechanism is the most fundamental process in Quantum Electrodynamics leading to the destruction of coherence, since it dominates for short times and because it is at work even in the electromagnetic field vacuum at zero temperature. It turns out that decoherence trough bremsstrahlung is very small for single electrons but extremely large for superpositions of many-particle states.
The processes of radiation damping and decoherence in Quantum Electrodynamics are studied from an open system's point of view. Employing functional techniques of field theory, the degrees of freedom of the radiation field are eliminated to obtain the influence phase functional which describes the reduced dynamics of the matter variables. The general theory is applied to the dynamics of a single electron in the radiation field. From a study of the wave packet dynamics a quantitative measure for the degree of decoherence, the decoherence function, is deduced. The latter is shown to describe the emergence of decoherence through the emission of bremsstrahlung caused by the relative motion of interfering wave packets. It is argued that this mechanism is the most fundamental process in Quantum Electrodynamics leading to the destruction of coherence, since it dominates for short times and because it is at work even in the electromagnetic field vacuum at zero temperature. It turns out that decoherence trough bremsstrahlung is very small for single electrons but extremely large for superpositions of many-particle states.
Photon number state representation, especially the single-photon state representation, and the coherent state representation are widely used to specify the state of a radiation field. The concept of density operator or density matrix is introduced in the process of calculating the expectation value of a quantum observable. People then introduce and distinguish the pure state and mixed state. The quantum states of composite system, especially the state of two-photon field, are studied by introducing an 2-D Hilbert space constructed as the direct or tensor product of the Hilbert spaces of two subsystems. A simple model for the creation of single-photon state and multi-photon state is given with details. The concepts of product state, entangled state, and mixed state are introduced and distinguished. Coherent states form a complete set of vector space. Similar to number states, coherent states can be used as a vector basis for characterizing radiation field, except coherent states are nonorthogonal vectors in general.