scholarly journals A FERMIONIC HODGE STAR OPERATOR

1999 ◽  
Vol 14 (15) ◽  
pp. 965-976
Author(s):  
ALFRED DAVIS ◽  
TRISTAN HÜBSCH
Keyword(s):  
Field Theory ◽  
Wave Function ◽  
Bilinear Form ◽  
Operator Representation ◽  
Exterior Calculus ◽  
Star Operation ◽  
Hodge Star Operator

A fermionic analogue of the Hodge star operation is shown to have an explicit operator representation in models with fermions, in space–times of any dimension. This operator realizes a conjugation (pairing) not used explicitly in field theory, and induces a metric in the space of wave function(al)s just as in exterior calculus. If made real (hermitian), this induced metric turns out to be identical to the standard one constructed using hermitian conjugation; the utility of the induced complex bilinear form remains unclear.

BILINEAR FORM AND SOLITON SOLUTIONS FOR THE COUPLED NONLINEAR KLEIN–GORDON EQUATIONS

2012 ◽  
Vol 26 (15) ◽  
pp. 1250057
Author(s):  
HE LI ◽  
XIANG-HUA MENG ◽  
BO TIAN
Keyword(s):  
Field Theory ◽  
Bilinear Form ◽  
Gordon Equation ◽  
Relativistic Quantum ◽  
Soliton Solutions ◽  
Relativistic Quantum Mechanics ◽  
Klein Gordon ◽  
Truncated Painlevé Expansion ◽  
Klein Gordon Equation ◽  
Singular Manifolds

With the coupling of a scalar field, a generalization of the nonlinear Klein–Gordon equation which arises in the relativistic quantum mechanics and field theory, i.e., the coupled nonlinear Klein–Gordon equations, is investigated via the Hirota method. With the truncated Painlevé expansion at the constant level term with two singular manifolds, the coupled nonlinear Klein–Gordon equations are transformed to a bilinear form. Starting from the bilinear form, with symbolic computation, we obtain the N-soliton solutions for the coupled nonlinear Klein–Gordon equations.

scholarly journals Crystal Field Theory And Magnetic Point Groups

1966 ◽  
Vol 19 (4) ◽  
pp. 519 ◽  
Keyword(s):  
Field Theory ◽  
Wave Function ◽  
Crystal Field ◽  
Energy Levels ◽  
Unitary Groups ◽  
Crystal Field Theory ◽  
Symmetry Properties ◽  
Point Groups

The author's previous work on the application of Wigner's theory of the coreps of non-unitary groups to the Shubnikov groups (magnetic groups) is here considered in relation to crystal field theory. Both the splitting of the energy levels and the symmetry properties of the wave function are considered in magnetic point groups. Examples of 4'mm' and 4m'm' are studied.

ON THE RELATION BETWEEN QUANTUM HYDRODYNAMICS AND CONVENTIONAL QUANTUM FIELD THEORY

1954 ◽  
Vol 32 (8) ◽  
pp. 530-537
Author(s):  
F. A. Kaempffer
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Wave Function ◽  
Classical Theory ◽  
Quantum Field ◽  
Quantum Hydrodynamics ◽  
Quantization Procedure ◽  
Nonrelativistic Theory ◽  
Hydrodynamical Description ◽  
Charged Medium

The conditions are examined under which the procedure of quantum hydrodynamics would be a consequence of the conventional quantization procedure, and vice versa. Using the classical nonrelativistic theory of a charged medium as an example, it is shown that the commutation rules of the two procedures differ by a factor 2, if in accordance with an idea by Geilikman the wave function of the classical theory is expanded as ψ = ψ0 + ψ1, with ψ0 a constant and [Formula: see text], and if terms of higher than second order in ψ1 are neglected in the hydrodynamical description of the theory.

ANYON EQUATION ON A TORUS

1992 ◽  
Vol 07 (23) ◽  
pp. 5797-5831 ◽  
Author(s):  
CHOON-LIN HO ◽  
YUTAKA HOSOTANI
Keyword(s):  
Field Theory ◽  
Wave Function ◽  
Essential Role ◽  
Wilson Line ◽  
Regular Function ◽  
Gauge Fields ◽  
Quantum Field ◽  
Many Body ◽  
Definition Of ◽  
Chern Simons

Starting from the quantum field theory of nonrelativistic matter on a torus interacting with Chern-Simons gauge fields, we derive the Schrödinger equation for an anyon system. The nonintegrable phases of the Wilson line integrals on a torus play an essential role. In addition to generating degenerate vacua, they enter in the definition of a many-body Schrödinger wave function in quantum mechanics, which can be defined as a regular function of the coordinates of anyons. It obeys a non-Abelian representation of the braid group algebra, being related to Einarsson’s wave function by a singular gauge transformation.

scholarly journals A novel view on successive quantizations, leading to increasingly more “miraculous” states

2019 ◽  
Vol 34 (23) ◽  
pp. 1950186 ◽  
Author(s):  
Matej Pavšič
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Wave Function ◽  
Wave Packet ◽  
Time Derivative ◽  
Point Particle ◽  
Order Equation ◽  
Quantum Field ◽  
First Order ◽  
Complex Wave

A series of successive quantizations is considered, starting with the quantization of a non-relativistic or relativistic point particle: (1) quantization of a particle’s position, (2) quantization of wave function, (3) quantization of wave functional. The latter step implies that the wave packet profiles forming the states of quantum field theory are themselves quantized, which gives new physical states that are configurations of configurations. In the procedure of quantization, instead of the Schrödinger first-order equation in time derivative for complex wave function (or functional), the equivalent second-order equation for its real part was used. In such a way, at each level of quantization, the equation a quantum state satisfies is just like that of a harmonic oscillator, and wave function(al) is composed in terms of the pair of its canonically conjugated variables.

scholarly journals A CONFORMAL FIELD THEORY DESCRIPTION OF THE PAIRED AND PARAFERMIONIC STATES IN THE QUANTUM HALL EFFECT

2000 ◽  
Vol 15 (27) ◽  
pp. 1679-1688 ◽  
Author(s):  
GERARDO CRISTOFANO ◽  
GIUSEPPE MAIELLA ◽  
VINCENZO MAROTTA
Keyword(s):  
Field Theory ◽  
Wave Function ◽  
Conformal Field Theory ◽  
Quantum Hall Effect ◽  
Ground State ◽  
Quantum Hall ◽  
Scalar Fields ◽  
Neutral Component ◽  
Conformal Field ◽  
Twisted Boundary Conditions

We extend the construction of the effective conformal field theory for the Jain hierarchical fillings proposed in Ref. 1 to the description of a quantum Hall fluid at nonstandard fillings [Formula: see text]. The chiral primary fields are found by using a procedure which induces twisted boundary conditions on the m scalar fields; they appear as composite operators of a charged and neutral component. The neutral modes describe parafermions and contribute to the ground state wave function with a generalized Pfaffian term. Correlators of Ne electrons in the presence of quasi-hole excitations are explicitly given for m=2.

FALLING INTO A BLACK HOLE

2008 ◽  
Vol 17 (03n04) ◽  
pp. 583-589 ◽  
Author(s):  
SAMIR D. MATHUR
Keyword(s):  
Field Theory ◽  
Black Hole ◽  
Wave Function ◽  
String Theory ◽  
Quantum Gravity ◽  
Definition Of

String theory tells us that quantum gravity has a dual description as a field theory (without gravity). We use the field theory dual to ask what happens to an object as it falls into the simplest black hole: the two-charge extremal hole. In the field theory description the wave function of a particle is spread over a large number of "loops," and the particle has a well-defined position in space only if it has the same "position" on each loop. For the infalling particle we find one definition of "same position" on each loop, but there is a different definition for outgoing particles and no canonical definition in general in the horizon region. Thus the meaning of "position" becomes ill-defined inside the horizon.

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