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We develop a general theory of non-equilibrium states based on the Keldysh formalism, in particular, for charged-particle systems under static uniform electromagnetic fields. The Dyson equation for the uniform stationary state is rewritten in a compact gauge-invariant form by using the Moyal product in the phase space of energy-momentum variables, which originally do not commute in the case of the conventional operator algebra. Expanding the Dyson equation in electromagnetic fields, a systematic method for the order-by-order calculation of linear and non-linear responses from the zeroth-order Green's functions is obtained. In particular, we find that for impurity problems, up to linear order in the electric field, the present approach provides a diagrammatic method for the St\u{r}eda formula. This approach also generalizes the semi-classical Boltzmann transport theory to fully quantum-mechanical and/or multi-component systems. In multi-component systems and/or for Hall transport phenomena, however, this quantum Boltzmann transport theory, constructed from the anti-symmetric combination of two different representations for the Dyson equation, does not uniquely specify the non-equilibrium state, but the symmetric combination is required. We demonstate the formalism to calculate longitudinal and Hall electric conductivities in an isotropic single-band electron system in the clean limit. It is found that the results are fully consistent with those obtained by Mott and Ziman in terms of the semi-classical Boltzmann transport theory.

We develop a general theory of non-equilibrium states based on the Keldysh formalism, in particular, for charged-particle systems under static uniform electromagnetic fields. The Dyson equation for the uniform stationary state is rewritten in a compact gauge-invariant form by using the Moyal product in the phase space of energy-momentum variables, which originally do not commute in the case of the conventional operator algebra. Expanding the Dyson equation in electromagnetic fields, a systematic method for the order-by-order calculation of linear and non-linear responses from the zeroth-order Green's functions is obtained. In particular, we find that for impurity problems, up to linear order in the electric field, the present approach provides a diagrammatic method for the St\u{r}eda formula. This approach also generalizes the semi-classical Boltzmann transport theory to fully quantum-mechanical and/or multi-component systems. In multi-component systems and/or for Hall transport phenomena, however, this quantum Boltzmann transport theory, constructed from the anti-symmetric combination of two different representations for the Dyson equation, does not uniquely specify the non-equilibrium state, but the symmetric combination is required. We demonstate the formalism to calculate longitudinal and Hall electric conductivities in an isotropic single-band electron system in the clean limit. It is found that the results are fully consistent with those obtained by Mott and Ziman in terms of the semi-classical Boltzmann transport theory.

New quantum modes of the free scalar field are derived in a special time-evolution picture that may be introduced in moving charts of de Sitter backgrounds. The wave functions of these new modes are solutions of the Klein-Gordon equation and energy eigenfunctions, defining the energy basis. This completes the scalar quantum mechanics where the momentum basis is well-known from long time. In this enlarged framework the quantization of the scalar field can be done in canonical way obtaining the principal conserved one-particle operators and the Green functions.

The gauge compensation fields induced by the differential operators of the Stueckelberg-Schr\"odinger equation are discussed, as well as the relation between these fields and the standard Maxwell fields. An action is constructed and the second quantization of the fields carried out using a constraint procedure. Some remarks are made on the properties of the second quantized matter fields.

For linear scalar field theories, I characterize those classical Hamiltonian vector fields which have self-adjoint operators as their quantum counterparts. As an application, it is shown that for a scalar field in curved space-time (in a Hadamard representation), a self-adjoint Hamiltonian for evolution along the unit timelike normal to a Cauchy surface exists only if the second fundamental form of the surface vanishes identically.

For linear scalar field theories, I characterize those classical Hamiltonian vector fields which have self-adjoint operators as their quantum counterparts. As an application, it is shown that for a scalar field in curved space-time (in a Hadamard representation), a self-adjoint Hamiltonian for evolution along the unit timelike normal to a Cauchy surface exists only if the second fundamental form of the surface vanishes identically.

Source: Digital Library of India Scanning Centre: IIAp, Bangalore Source Library: Indian Institute Of Astrophysics Date Accessioned: 7/7/2015 6:57 The Digital Library of India was a project under the auspices of the Government of India.

Source: Digital Library of India Scanning Centre: IIAp, Bangalore Source Library: Indian Institute Of Astrophysics Date Accessioned: 7/7/2015 6:57 The Digital Library of India was a project under the auspices of the Government of India.

We present a theory for rigorous quantum scattering calculations of probabilities for chemical reactions of atoms with diatomic molecules in the presence of an external electric field. The approach is based on the fully uncoupled basis set representation of the total wave function in the space-fixed coordinate frame, the Fock-Delves hyperspherical coordinates and adiabatic partitioning of the total Hamiltonian of the reactive system. The adiabatic channel wave functions are expanded in basis sets of hyperangular functions corresponding to different reaction arrangements and the interactions with external fields are included in each chemical arrangement separately. We apply the theory to examine the effects of electric fields on the chemical reactions of LiF molecules with H atoms and HF molecules with Li atoms at low temperatures and show that electric fields may enhance the probability of chemical reactions and modify reactive scattering resonances by coupling the rotational states of the reactants. Our preliminary results suggest that chemical reactions of polar molecules at temperatures below 1 K can be selectively manipulated with dc electric fields and microwave laser radiation.

Review of the two volume set "The Quantum Theory of Fields" by S. Weinberg is presented.

Review of the two volume set "The Quantum Theory of Fields" by S. Weinberg is presented.

Recent advances on quantum foundations achieved the derivation of free quantum field theory from general principles, without referring to mechanical notions and relativistic invariance. From the aforementioned principles a quantum cellular automata (QCA) theory follows, whose relativistic limit of small wave-vector provides the free dynamics of quantum field theory. The QCA theory can be regarded as an extended quantum field theory that describes in a unified way all scales ranging from an hypothetical discrete Planck scale up to the usual Fermi scale. The present paper reviews the elementary automaton theory for the Weyl field, and the composite automata for Dirac and Maxwell fields. We then give a simple analysis of the dynamics in the momentum space in terms of a dispersive differential equation for narrowband wave-packets, and some account on the position space description in terms of a discrete path-integral approach. We then review the phenomenology of the free-field automaton and consider possible visible effects arising from the discreteness of the framework. We conclude introducing the consequences of the automaton distorted dispersion relation, leading to a deformed Lorentz covariance and to possible effects on the thermodynamics of ideal gases.

Recent advances on quantum foundations achieved the derivation of free quantum field theory from general principles, without referring to mechanical notions and relativistic invariance. From the aforementioned principles a quantum cellular automata (QCA) theory follows, whose relativistic limit of small wave-vector provides the free dynamics of quantum field theory. The QCA theory can be regarded as an extended quantum field theory that describes in a unified way all scales ranging from an hypothetical discrete Planck scale up to the usual Fermi scale. The present paper reviews the elementary automaton theory for the Weyl field, and the composite automata for Dirac and Maxwell fields. We then give a simple analysis of the dynamics in the momentum space in terms of a dispersive differential equation for narrowband wave-packets, and some account on the position space description in terms of a discrete path-integral approach. We then review the phenomenology of the free-field automaton and consider possible visible effects arising from the discreteness of the framework. We conclude introducing the consequences of the automaton distorted dispersion relation, leading to a deformed Lorentz covariance and to possible effects on the thermodynamics of ideal gases.

Recent advances on quantum foundations achieved the derivation of free quantum field theory from general principles, without referring to mechanical notions and relativistic invariance. From the aforementioned principles a quantum cellular automata (QCA) theory follows, whose relativistic limit of small wave-vector provides the free dynamics of quantum field theory. The QCA theory can be regarded as an extended quantum field theory that describes in a unified way all scales ranging from an hypothetical discrete Planck scale up to the usual Fermi scale. The present paper reviews the elementary automaton theory for the Weyl field, and the composite automata for Dirac and Maxwell fields. We then give a simple analysis of the dynamics in the momentum space in terms of a dispersive differential equation for narrowband wave-packets, and some account on the position space description in terms of a discrete path-integral approach. We then review the phenomenology of the free-field automaton and consider possible visible effects arising from the discreteness of the framework. We conclude introducing the consequences of the automaton distorted dispersion relation, leading to a deformed Lorentz covariance and to possible effects on the thermodynamics of ideal gases.

In standard quantum field theory, the one-particle states are classified by unitary representations of the Poincar\'e group, whereas the causal fields' classification employs the finite dimensional (non-unitary) representations of the (homogeneous) Lorentz group. A natural question arises - why the fields are not allowed to transform nontrivially under translations? We investigate this issue by considering the fields that transform under the full representation of the Poincar\'e group. It follows that such fields can be consistently constructed, although the Lagrangians that describe them necessarily exhibit explicit dependence on the space-time coordinates. The two examples of the Poincar\'e-spinor and the Poincar\'e-vector fields are considered in details. The inclusion of Yang--Mills type interactions is considered on the simplest example of the U(1) gauge theory. The generalization to the non-abelian case is straightforward so long as the action of the gauge group on fields is independent of the action of the Poincar\'e group. This is the case for all the known interactions but gravity.

In standard quantum field theory, the one-particle states are classified by unitary representations of the Poincar\'e group, whereas the causal fields' classification employs the finite dimensional (non-unitary) representations of the (homogeneous) Lorentz group. A natural question arises - why the fields are not allowed to transform nontrivially under translations? We investigate this issue by considering the fields that transform under the full representation of the Poincar\'e group. It follows that such fields can be consistently constructed, although the Lagrangians that describe them necessarily exhibit explicit dependence on the space-time coordinates. The two examples of the Poincar\'e-spinor and the Poincar\'e-vector fields are considered in details. The inclusion of Yang--Mills type interactions is considered on the simplest example of the U(1) gauge theory. The generalization to the non-abelian case is straightforward so long as the action of the gauge group on fields is independent of the action of the Poincar\'e group. This is the case for all the known interactions but gravity.

The book is based on a new (original) theory which argues the possibility of a cold genesis of particles and of fundamental fields, in the Protouniverse’s period, by primordial gravistars, using the concept of sub-quantum fluid, explaining the elementary particle and the fundamental fields cold genesis with ideal unitary pre-quantum particle’ models of simple or composite chiral soliton type, formed at T→0K from confined “dark energy” in a cascade vortex process, according to the ideal fluids mechanics applied to the particle soliton vortex. The electro-magnetic and the gravity-static and gravity-dynamic fields are described by an unitary model of charge and by an unitary field equation.  The exponential form of the nuclear potential is theoretically found through a mesonic and baryonic model of degenerate electrons and an Eulerian expression, as being generated by the vortexial dynamic pressure inside the nucleonic quantum volume. The weak force is explained by a dynamic model of neutron with intrinsic vibration and the particle disintegration is explained as a result of intrinsic vibration of particles generated by vibrations of current mass quarks formed as B-E condensate cluster of quasi-electrons, by gammons confining in very strong magnetic field, of a gravistar or a magnetar star.  For a phenomenological model of cosmic expansion, by the dependency of the G-gravitation constant on the etheronic local density, the physical cause of the cosmic expansion results as a force of pressure difference of etheronic winds coming from the ultrahot stellary structures having an antigravitic charge given by destroyed particles, the speed of expansion resulting with a semi-sinusoidal variation.  The theory can explain also phenomenological, some known specific effects, like the magneto-electric and the magneto-mechanic effects.

The Quantum Theory Of Fields Volume 1 Weinberg

The Quantum Theory Of Fields Volume 1 Weinberg

We present a method to engineer the unitary charge conjugation operator, as given by quantum field theory, in the highly controlled context of quantum optics, thus allowing one to simulate the creation of charged particles with well-defined momenta simultaneously with their respective antiparticles. Our method relies on trapped ions driven by a laser field and interacting with a single mode of a light field in a high Q cavity.

We present a method to engineer the unitary charge conjugation operator, as given by quantum field theory, in the highly controlled context of quantum optics, thus allowing one to simulate the creation of charged particles with well-defined momenta simultaneously with their respective antiparticles. Our method relies on trapped ions driven by a laser field and interacting with a single mode of a light field in a high Q cavity.

We present a method to engineer the unitary charge conjugation operator, as given by quantum field theory, in the highly controlled context of quantum optics, thus allowing one to simulate the creation of charged particles with well-defined momenta simultaneously with their respective antiparticles. Our method relies on trapped ions driven by a laser field and interacting with a single mode of a light field in a high Q cavity.