摘要:

AbstractStarting with the most general Lagrangian of the fourth‐order non‐linear sigma model in four space‐time dimensions, we calculate the one‐loop, on shell ultra‐violet‐divergent part of the effective action. The formalism is based on the background field method and the generalised Schwinger De Witt technique. The multiplicatively renormalisable case is investigated in some detail. The renormalisation group equations are obtained, and the conditions for a realisation of asymptotic freedom are

ISSN:0015-8208    

DOI:10.1002/prop.2190390102

出版商:WILEY‐VCH Verlag    

年代:1991

数据来源: WILEY

摘要:

AbstractA statistical mechanical theory is developed for gas‐phase bimolecular (binary) reactions:AB⇌A+B. Based on the activated‐complex hypotheses, and expression for the association rate constantkais derived:ka=k*AB* → AB(QAB*/qA+B), wherek*AB* →ABis the rate constant for the transition from the activated stateAB* to the molecular stateAB, andqxis the equilibrium occupation probability for state X. The three states (AB, AB*, A +B) are defined by three regions of the energyseparation plane for the relative motion of the reactant pair (A,B). If the interatomic potential has a critical barrier ϵcat separationrcand an attractive well with depth ϵb(ϵc, ϵb>kBT) computations of theqAB*/qA +Bgenerate an Arrhenius‐Boltzmann factor exp (—ϵc/kBT). The virtual rate constantk*AB* →ABis calculated by assuming that the reactant pair reaching the activated stateAB* with the separationrcmoves on to the molecular stateABonly if it loses part of its radial kinetic energy with the aid of third body (catalyst or collision) and is trapped by the potential well. With no catalysts present, this constant is approximately given byk*AB* →AB=πd′2v′ R′−3, wherev′ is the thermal center‐of‐mass speed, andd′ andR′ are respectively the collision‐sphere radius and the mean distance betweenAB* and any molecule (A, B, AB orAB*). For binary dissociation, the rate constantkdis given bykd=k*AB* →A+BqAB*/qAB), which generates exp [—(ϵc+ ϵb)/kBT]. A catalyst for binary reaction is assumed to act as a mediator, facilitating the energy exchange between the radial and rotational modes of motion. Additionally for association only, it also acts as a confinement agent, preventing the pair from flying away from each other. Connections with the collision theory and the

ISSN:0015-8208    

DOI:10.1002/prop.2190390103

出版商:WILEY‐VCH Verlag    

年代:1991

数据来源: WILEY

摘要:

AbstractThe object of this paper is to apply Takahashi's Galilei‐invariant field theory to the derivation of the Clebsch transformation of hydrodynamic equations. In this paper, only normal fluids are considered, while in the second paper we will develop a field theory of superfluid hydrodynamics. Given view point adopted here, the fundamental objects of the theory are Galilei scalars which are invariant under the Galilei transformation. In terms of such scalars, the Lagrangian density is written explicitly. It is shown how the Clebsch transformation can be reformulated from a field theoretical viewpoin

ISSN:0015-8208    

DOI:10.1002/prop.2190390104

出版商:WILEY‐VCH Verlag    

年代:1991

数据来源: WILEY

摘要:

AbstractThe first paper in this series developed a field‐theoretical approach to hydrodynamics. The objective of this second paper is to extend that formalism to superfluid hydrodynamics. Given the viewpoint adopted here, the fundamental objectives of the theory are the superfluid order‐parameter function, Ψ(x), the collective and the individual motions, in terms of which one can define Galilei invariants. Basic to the present theory is that the Schrödinger field Ψ(x) can by expressed in terms of the Galilei invariants (ϕn(x), ϕs(x)) and the phase ϕ(x) as φ(x) = exp {(im/h) ϕ(x)}F[x: Ψ(x), ϕn(x), ϕs(x), φ(x)] where the complex field φ(x) describes the individual motions (or is the asymptotic field). A plausible Lagrangian density, which in invariant, under the Galilei boost with a constant velocity, then permits the derivation of the equation of motion for the

ISSN:0015-8208    

DOI:10.1002/prop.2190390105

出版商:WILEY‐VCH Verlag    

年代:1991

数据来源: WILEY

摘要:

AbstractThe existence of different Lagrangian functions for the same dynamical vector field is studied using the methods of symplectic mechanics. The concept of Lagrangeoid transformation is introduced and its relation with the theory of bi‐Hamiltonian systems analyzed. The relation between equivalent (non‐gauge equivalent) Lagrangian formulations inTQand their associated Hamiltonian dynamical systems inT*Qis developed and, finally, the Noether theorem is conside

ISSN:0015-8208    

DOI:10.1002/prop.2190390106

出版商:WILEY‐VCH Verlag    

年代:1991

数据来源: WILEY

摘要:

AbstractQuantum tunneling in one spatial dimension in the presence of time‐dependent potentials is investigated theoretically. First, a general multichannel formulation of the problem is given for harmonic time‐dependence. The case of an oscillatory delta‐function potential of constant strength is discussed at length and specific numerical calculations are presented for the reflection and transmission coefficients. Then other exactly solvable time‐dependent potentials are obtained by carrying out successive unitary transformations. As an example of this class, a delta‐function potential with time‐dependent strength and boundary conditions is studied. Finally tunneling time‐delay for time‐dependent potentials is formulated in the multichannel situation, and also the concept of first passage time for the decay of a wave packet confined to one well of a double well potential is generalized for the case of time‐dependent barrier and bo

ISSN:0015-8208    

DOI:10.1002/prop.2190390107

出版商:WILEY‐VCH Verlag    

年代:1991

数据来源: WILEY

ISSN:0015-8208    

DOI:10.1002/prop.2190390101

出版商:WILEY‐VCH Verlag    

年代:1991

数据来源: WILEY