COMPLEX MASS FERMIONIC FIELDS

1994 ◽  
Vol 09 (12) ◽  
pp. 2103-2115 ◽  
Author(s):  
D.G. BARCI ◽  
L.E. OXMAN
Keyword(s):  
Degrees Of Freedom ◽  
Order Equation ◽  
Complex Conjugate ◽  
Zero Energy ◽  
Natural Representation ◽  
Symmetric State ◽  
Fermionic Field ◽  
Fermionic Fields ◽  
Real Mass ◽  
Mass Case

We consider a fermionic field obeying a second order equation containing a pair of complex conjugate mass parameters. After obtaining a natural representation for the different degrees of freedom, we are able to construct a unique vacuum as the more symmetric state (zero energy-momentum, charge and spin). This representation, unlike the real mass case, is not holomorphic in the Grassmann variables. The vacuum eigenstate allows the calculation of the field propagator which turns out to be half advanced plus half retarded.

scholarly journals A novel approach to the computation of one-loop three- and four-point functions: I. The real mass case

2019 ◽  
Vol 2019 (11) ◽  
Author(s):  
J Ph Guillet ◽  
E Pilon ◽  
Y Shimizu ◽  
M S Zidi
Keyword(s):  
Building Blocks ◽  
The Real ◽  
Alternative Method ◽  
Novel Approach ◽  
Reduction Methods ◽  
Real Mass ◽  
Novel Method ◽  
Algebraic Reduction ◽  
The One ◽  
Mass Case

Abstract This article is the first of a series of three presenting an alternative method of computing the one-loop scalar integrals. This novel method enjoys a couple of interesting features as compared with the method closely following ’t Hooft and Veltman adopted previously. It directly proceeds in terms of the quantities driving algebraic reduction methods. It applies to the three-point functions and, in a similar way, to the four-point functions. It also extends to complex masses without much complication. Lastly, it extends to kinematics more general than that of the physical, e.g., collider processes relevant at one loop. This last feature may be useful when considering the application of this method beyond one loop using generalized one-loop integrals as building blocks.

scholarly journals PHYSICAL SPECTRUM FROM CONFINED EXCITATIONS IN A YANG–MILLS-INSPIRED TOY MODEL

2013 ◽  
Vol 28 (10) ◽  
pp. 1350034 ◽  
Author(s):  
M. A. L. CAPRI ◽  
D. DUDAL ◽  
M. S. GUIMARAES ◽  
L. F. PALHARES ◽  
S. P. SORELLA
Keyword(s):  
Field Theory ◽  
Bound States ◽  
Gauge Theories ◽  
Spectral Representation ◽  
Complex Conjugate ◽  
Meson Mass ◽  
Yang Mills ◽  
Physical Spectrum ◽  
Real Mass ◽  
Particle Interpretation

We study a toy model for an interacting scalar field theory in which the fundamental excitations are confined in the sense of having unphysical, positivity-violating propagators, a fact tracing back to a decomposition of these in propagators with complex conjugate mass poles (the so-called i-particles). Similar two-point functions show up in certain approaches to gluon or quark propagators in Yang–Mills gauge theories. We investigate the spectrum of our model and show that suitable composite operators may be constructed having a well-defined Källén–Lehmann spectral representation, thus allowing for a particle interpretation. These physical excitations would correspond to the "mesons" of the model, the latter being bound states of two unphysical i-particles. The meson mass is explicitly estimated from the pole emerging in a resummed class of diagrams. The main purpose of this paper is thus to explicitly verify how a real mass pole can and does emerge out of constituent i-particles that have complex masses.

scholarly journals Cosmological model with fermion and tachyon fields interacting via Yukawa-type potential

2016 ◽  
Vol 31 (06) ◽  
pp. 1650039 ◽  
Author(s):  
Marlos O. Ribas ◽  
Fernando P. Devecchi ◽  
Gilberto M. Kremer
Keyword(s):  
Dark Energy ◽  
Cosmological Model ◽  
Matter Field ◽  
Fermionic Field ◽  
Tachyonic Field ◽  
Fermionic Fields ◽  
The Universe ◽  
Type Potential

A model for the universe with tachyonic and fermionic fields interacting through a Yukawa-type potential is investigated. It is shown that the tachyonic field answers for the initial accelerated regime and for the subsequent decelerated regime so that it behaves as an inflaton at early times and as a matter field at intermediate times, while the fermionic field has the role of a dark energy constituent, since it leads to an accelerated regime at later times. The interaction between the fields via a Yukawa-type potential controls the duration of the decelerated era, since a stronger coupling makes a shorter decelerated period.

scholarly journals Unification of massless field equations solutions for any spin

2021 ◽  
Author(s):  
Sergio Hojman ◽  
Felipe Asenjo
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Potential Functions ◽  
Field Equations ◽  
Fermionic Field ◽  
Massless Field ◽  
Coupled Equations ◽  
Klein Gordon ◽  
Fermionic Fields ◽  
Derivatives Of

Abstract A unification in terms of exact solutions for massless Klein–Gordon, Dirac, Maxwell, Rarita– Schwinger, Einstein, and bosonic and fermionic fields of any spin is presented. The method is based on writing all of the relevant dynamical fields in terms of products and derivatives of pre–potential functions, which satisfy d’Alambert equation. The coupled equations satisfied by the pre–potentials are non-linear. Remarkably, there are particular solutions of (gradient) orthogonal pre–potentials that satisfy the usual wave equation which may be used to construct exact non–trivial solutions to Klein–Gordon, Dirac, Maxwell, Rarita–Schwinger, (linearized and full) Einstein and any spin bosonic and fermionic field equations, thus giving rise to an unification of the solutions of all massless field equations for any spin. Some solutions written in terms of orthogonal pre–potentials are presented. Relations of this method to previously developed ones, as well as to other subjects in physics are pointed out.

scholarly journals Simulink and Simelectronics based Position Control of a Coupled Mass-Spring Damper Mechanical System

2018 ◽  
Vol 8 (5) ◽  
pp. 3636
Author(s):  
Oyetola O. K. ◽  
Olaluwoye O. O.
Keyword(s):  
Mathematical Model ◽  
Degrees Of Freedom ◽  
Position Control ◽  
Lagrange Equation ◽  
Complex Conjugate ◽  
Conjugate Pair ◽  
Modeling And Control ◽  
Position Errors ◽  
Result Analysis ◽  
Mass Spring

This paper presents the use of Simelectronics Program for modeling and control of a two degrees-of freedom coupled mass-spring-damper mechanical system.The aims of this paper are to establish a mathematical model that represents the dynamic behaviour of a coupled mass-spring damper system and effectively control the mass position using both Simulink and Simelectronics.The mathematical model is derived based on the augmented Lagrange equation and to simulate the dynamic accurately a PD controller is implemented to compensate for the oscillation sustained by the system as a result of the complex conjugate pair poles near to the imaginary axis.The input force has been subjected to an obstacle to mimic actual challenges and to validate the mathematical model a Simulink and Simelectronics models were developed, consequently, the results of the models were compared. According to the result analysis, the controller tracked the position errors and stabilized the positions to zero within a settling time of 6.5sec and significantly reduced the overshoot by 99.5% and 99. 7% in Simulink and Simelectronics respectively. Furthermore, it is found that Simelectronics model proved to be capable having advantages of simplicity, less time-intense and requires no mathematical model over the Simulink approach.

scholarly journals Adinkra foundation of component decomposition and the scan for superconformal multiplets in 11D, $$ \mathcal{N} $$ = 1 superspace

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
S. James Gates ◽  
Yangrui Hu ◽  
S.-N. Hazel Mak
Keyword(s):  
Computational Efficiency ◽  
Degrees Of Freedom ◽  
Component Decomposition ◽  
Physics Literature ◽  
Fermionic Fields ◽  
Component Field ◽  
Scalar Superfield ◽  
First Time

Abstract For the first time in the physics literature, the Lorentz representations of all 2,147,483,648 bosonic degrees of freedom and 2,147,483,648 fermionic degrees of freedom in an unconstrained eleven dimensional scalar superfield are presented. Comparisons of the conceptual bases for this advance in terms of component field, superfield, and adinkra arguments, respectively, are made. These highlight the computational efficiency of the adinkra-based approach over the others. It is noted at level sixteen in the 11D, $$ \mathcal{N} $$ N = 1 scalar superfield, the {65} representation of SO(1,10), the conformal graviton, is present. Thus, adinkra-based arguments suggest the surprising possibility that the 11D, $$ \mathcal{N} $$ N = 1 scalar superfield alone might describe a Poincaré supergravity prepotential or semi-prepotential in analogy to one of the off-shell versions of 4D, $$ \mathcal{N} $$ N = 1 superfield supergravity. We find the 11D, $$ \mathcal{N} $$ N = 1 scalar superfield contains 1,494 bosonic fields, 1,186 fermionic fields, and a maximum number of 29,334 links connecting them via orbits of the supercharges.

UNITARITY AND COMPLEX MASS FIELDS

1993 ◽  
Vol 08 (18) ◽  
pp. 3185-3198 ◽  
Author(s):  
C. G. BOLLINI ◽  
L. E. OXMAN
Keyword(s):  
Absorptive Part ◽  
Vacuum Expectation ◽  
Complex Conjugate ◽  
Expectation Values ◽  
Self Energy ◽  
Causal Function ◽  
S Matrix ◽  
Complex Mass ◽  
Real Mass ◽  
Higher Order Equation

We consider a field obeying a simple higher order equation with a real mass and two complex conjugate mass parameters. The evaluation of vacuum expectation values leads to the propagators, which are (resp.) a Feynman causal function and two complex conjugate Wheeler–Green functions (half retarded plus half advanced). By means of the computation of convolutions, we are able to show that the total self-energy has an absorptive part which is only due to the real mass. In this way it is shown that this diagram is compatible with unitarity and the elimination of free complex-mass asymptotic states from the set of external legs of the S-matrix. It is also shown that the complex masses act as regulators of ultraviolet divergences.

Non-Conforming Solid Elements for the Analyses of Bending Deformation of Isotropic/Orthotropic Materials with the Smallest D.O.F.

2003 ◽  
Vol 17 (08n09) ◽  
pp. 1863-1869 ◽  
Author(s):  
Y. D. Kwon ◽  
N. S. Goo ◽  
T. H. Yun
Keyword(s):  
Material Properties ◽  
Degrees Of Freedom ◽  
Orthotropic Materials ◽  
Zero Energy ◽  
Orthotropic Plates ◽  
Shear Deformations ◽  
Bending Deformation ◽  
Forced Motion ◽  
Solid Element ◽  
Fine Mesh

This paper proposes both a 3-D 10-node equivalent solid element and a 2-D 5-node equivalent solid element. These proposed elements have the smallest number of degree of freedom among 3-D/2-D solid elements, taking into consideration bending deformation as well as extensional and shear deformations of solids. The proposed elements exhibit greater bending stiffness than the conventional 2-D/3-D solid elements, due to the reduction of degrees of freedom. This phenomenon of greater stiffness was corrected by using a modification of Gauss sampling points. The quantity of modification is expressed as a function of material properties. Adopting this kind of modification, we can show that even the conventional 4-node elements can be applied to the analysis of bending problem successfully in proper fine mesh. The proposed elements pass the patch test and have no spurious zero energy modes. The effectiveness of MQ10 element (Q10 with the modification) is tested in several examples. The results of static and free vibration analyses of isotropic/orthotropic plates using MQ10 elements show good agreements with those using 20-node element. In addition, damped/undamped forced motion analyses using MQ10 elements were carried out, and compared with those of a 20-node element.

scholarly journals Investigation into the control strategy for a long spine of Edinburgh Duck modules, using an efficient numerical model

2020 ◽  
Vol 3 (3) ◽  
pp. 145-154
Author(s):  
Alfred Cotten ◽  
David I. M. Forehand
Keyword(s):  
Numerical Model ◽  
Degrees Of Freedom ◽  
Control Method ◽  
Complex Conjugate ◽  
Control Force ◽  
Power Extraction ◽  
Absorbed Power ◽  
Added Benefit ◽  
Joint Motions ◽  
Motion Constraint

An efficient numerical model of a spine of ten Edinburgh duck modules is developed. The spine joints and duck modules are modelled using a linear approach based on the theory of generalized modes, which mitigates the need for a more computationally expensive time- domain solver. This approach also allows for computation of the shear forces acting on the spine joints, and has the added benefit of enabling the use of complex conjugate control. The resulting hydrodynamic model is verified for a three duck spine against an alternative implementation that uses a nonlinear multibody solver to enforce the joint motions. A conservative weighted motion constraint is imposed on the controlled degrees of freedom of the ten duck spine, in order to ensure results stay within the bounds of the linear theory. Pertinent sections of the theory underpinning the constrained complex conjugate control method are elaborated upon for the case in which not all degrees of freedom are controlled. An implementation of this control method for a solo duck is compared against a result from the literature, in order to confirm the suitability of the choice of duck design in this study. The control force coefficients that maximise the absorbed power, subject to the motion constraint, are computed for the ten duck spine over a range of wave periods and wave heading angles. The resulting dynamics of the spine of ducks are explored, with particular emphasis on aspects related to the power extraction and forces acting within the system.

scholarly journals Quadratic gravity and restricted Weyl symmetry

2021 ◽  
pp. 2150139
Author(s):  
Arata Kamimura ◽  
Ichiro Oda
Keyword(s):  
Gauge Symmetry ◽  
Degrees Of Freedom ◽  
Minkowski Spacetime ◽  
Static Condition ◽  
Gauge Parameter ◽  
Zero Energy ◽  
Quadratic Gravity ◽  
Weyl Symmetry ◽  
Dynamical Degrees ◽  
The Relationship

In this paper, we investigate the relationship between quadratic gravity and a restricted Weyl symmetry where a gauge parameter [Formula: see text] of Weyl transformation satisfies a constraint [Formula: see text] in a curved spacetime. First, we briefly review a model with a restricted gauge symmetry on the basis of QED, where a [Formula: see text] gauge parameter [Formula: see text] obeys a similar constraint [Formula: see text] in a flat Minkowski spacetime, and explain that the restricted gauge symmetry removes one on-shell mode of gauge field, which together with the Feynman gauge leaves only two transverse polarizations as physical states. Next, it is shown that the restricted Weyl symmetry also eliminates one component of a dipole field in quadratic gravity around a flat Minkowski background, leaving only a single scalar state. Finally, we show that the restricted Weyl symmetry cannot remove any dynamical degrees of freedom in static background metrics by using the zero-energy theorem of quadratic gravity. This fact also holds for the Euclidean background metrics without imposing the static condition.

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