Two-dimensional Spacetime Research Articles

Super Yang–Mills theory from nonlinear supersymmetry

The relation between a nonlinear supersymmetric (NLSUSY) theory and a SUSY Yang–Mills (SYM) theory is studied for N=3 SUSY in two-dimensional space–time. We explicitly show the NL/L SUSY relation for the (pure) SYM theory by means of cancellations among Nambu–Goldstone fermion self-interaction terms.

Determination of two-dimensional space–time correlations in jet flows using simultaneous PIV and LDV measurements

The two-dimensional space–time turbulence statistics of free shear jet flows in the form of the two-point velocity correlation tensor are important for aeroacoustic noise source modelling based on the acoustic analogy approach. This paper presents a direct application of the Point-Referenced Global Correlation (PRGC) technique to measure the components of this correlation tensor for a sector of the flow field in two jet configurations. The PRGC approach combines single point and global measurement techniques and enables two-point space–time correlations over a region of the flow to be obtained. The technique is applied to a single stream jet and a co-axial coplanar jet at a Mach number of 0.24 using commercial Laser Doppler velocimetry (LDV) and low-speed particle image velocimetry (PIV) systems. Results for the one-dimensional correlations are shown to compare well with two-point measurements. The results for the two-dimensional space–time correlations are presented and the characteristics for both configurations discussed.

Quantum radiation force on the moving mirror of a cavity, with Dirichlet and Neumann boundary conditions for a vacuum, finite temperature, and a coherent state

We consider a real massless scalar field inside a cavity with a moving mirror in a two-dimensional spacetime, satisfying the Dirichlet or Neumann boundary condition at the instantaneous position of the boundaries, for an arbitrary and relativistic law of motion. Considering an arbitrary initial field state, we show that the exact value of the energy density in the cavity can be obtained by tracing back a sequence of null lines, connecting the value of the energy density at the given spacetime point to a certain known value of the energy density at a point in the region where the initial field modes are not affected by the boundary motion. We obtain the particular formulas for the energy density of the field and the quantum force acting on the boundaries for a vacuum, thermal, and a coherent state. We thus generalize a previous result in literature [17], where this problem is approached for only one mirror. For the particular cases of vacuum and Dirichlet boundary condition, nonrelativistic velocities, or in the limit of large length of the cavity, our results coincide with those found in the literature.

Solving two-dimensional space-time dependent multi-group diffusion equations with SOR method

In this research, solution of two-dimensional space-time diffusion equations with SOR (Successive Over Relaxation) method has been proposed. SOR method is chosen because this method is one of iterative methods that does not require to define whole element matrix. The results of this research have been compared with the results of TWIGL two-dimensional problems. The research is divided in two cases: homogeneous and heterogeneous case. Homogeneous case has been inserted by step reactivity. Heterogeneous case has been inserted by step reactivity, ramp reactivity and sinusoidal reactivity. Difference of thermal neutron flux varies with reactivity insertion in heterogeneous cases, although number of mesh and error tolerance is similar between step and ramp reactivity insertion cases. In general, the results of simulations are in agreement with data from reference. In the case of sinusoidal reactivity insertion, the pattern of flux distribution is repeated in interval of period with increased amplitude. SOR is an effective method to solve two-dimensional space-time multi-group diffusion equations.

Functional Integrals and Quantum Fluctuations on Two-Dimensional Noncommutative Space-Time

The generalized Thirring model with impurity coupling is defined on two-dimensional noncommutative space-time, a modified propagator and free energy are derived by means of functional integrals method. Moreover, quantum fluctuations and excitation energies are calculated on two-dimensional black hole and soliton background.

Time evolution of the energy density inside a one-dimensional non-static cavity with a vacuum, thermal and a coherent state

We study the time evolution of the energy density for a real massless scalar field in a two-dimensional spacetime, inside an expanding (not oscillating) cavity, and also the force exerted by the field on the moving boundary. Our calculations are based on the exact numerical approach proposed by Cole and Schieve. Considering Neumann and Dirichlet boundary conditions, we investigate the following initial states of the field: vacuum, thermal and the coherent state.

Quantum radiation force on a moving mirror for a thermal and a coherent field

We consider a real massless scalar field in a two-dimensional spacetime, satisfying Dirichlet or Neumann boundary condition at the instantaneous position of a moving boundary. For a relativistic particular motion proposed by Walker-Davies (J. Phys. A, 15, L477 (1982)), we obtain the exact formulas for the radiation force on the boundary for thermal and coherent states.

Quantum mechanics in a two-dimensional spacetime: What is a wavefunction?

Conventional quantum mechanics specifies the mathematical properties of wavefunctions and relates them to physical experiments by invoking the Born postulate. There is no known direct connection between wavefunctions and any external physical object. However, in the case of a two-dimensional spacetime there is a completely classical context for wavefunctions where the connection with an external reality is transparent and unambiguous. By examining this case, we show how a classical stochastic process assembles a Dirac wavefunction based solely on the detailed counting of reversible paths. A direct comparison of how a related process assembles a Probability Density Function reveals both how and why PDFs and wavefunctions differ, including the ubiquitous implication of complex numbers for the latter. The appearance of wavefunctions in a context that is free of the complexities of quantum mechanics suggests the study of such models may shed some light on interpretive issues.

N = 2 SUSY QED IN NONLINEAR/LINEAR SUSY RELATION

We show systematically the relation between an N = 2 nonlinear supersymmetric (NLSUSY) model and an N = 2 SUSY QED theory by means of the superfield formulation in two-dimensional spacetime without imposing a priori any special gauge conditions for a gauge superfield.

Superconducting loop quantum gravity and the cosmological constant

We argue that the cosmological constant is exponentially suppressed in a candidate ground state of loop quantum gravity as a nonperturbative effect of a holographic Fermi-liquid theory living on a two-dimensional spacetime. Ashtekar connection components, corresponding to degenerate gravitational configurations breaking large gauge invariance and CP symmetry, behave as composite fermions that condense as in Bardeen–Cooper–Schrieffer theory of superconductivity. Cooper pairs admit a description as wormholes on a de Sitter boundary.

Topological field theories inn-dimensional spacetimes and Cartan’s equations

Action principles of the BF type for diffeomorphism invariant topological field theories living in n-dimensional spacetime manifolds are presented. Their construction is inspired by Cuesta and Montesinos' recent paper where Cartan's first and second structure equations together with first and second Bianchi identities are treated as the equations of motion for a field theory. In opposition to that paper, the current approach involves also auxiliary fields and holds for arbitrary n-dimensional spacetimes. Dirac's canonical analysis for the actions is detailedly carried out in the generic case and it is shown that these action principles define topological field theories, as mentioned. The current formalism is a generic framework to construct geometric theories with local degrees of freedom by introducing additional constraints on the various fields involved that destroy the topological character of the original theory. The latter idea is implemented in two-dimensional spacetimes where gravity coupled to matter fields is constructed out, which has indeed local excitations.

On Wess–Zumino gauge

In the relation between the linear (L) supersymmetry (SUSY) representation and the nonlinear (NL) SUSY representation we discuss the role of the Wess–Zumino gauge. We show in two-dimensional spacetime that a spontaneously broken LSUSY theory with mass and Yukawa interaction terms for a minimal off-shell vector supermultiplet is obtained from a general superfield without imposing any special gauge conditions in N=2 NL/L SUSY relation.

Quantum radiation force on a moving mirror with Dirichlet and Neumann boundary conditions for a vacuum, finite temperature, and a coherent state

We consider a real massless scalar field in a two-dimensional spacetime, satisfying Dirichlet or Neumann boundary condition at the instantaneous position of a moving boundary. For a relativistic law of motion, we show that Dirichlet and Neumann boundary conditions yield the same radiation force on a moving mirror when the initial field state is invariant under time translations. We obtain the exact formulas for the energy density of the field and the radiation force on the boundary for vacuum, thermal, coherent, and squeezed states. In the nonrelativistic limit, our results coincide with those found in the literature.

ON N = 2 SUPERFIELD FOR N = 2 VECTOR SUPERMULTIPLET IN TWO-DIMENSIONAL SPACETIME

We focus on the superfield formulation for an N = 2 vector supermultiplet in two-dimensional spacetime and explicitly show that the Wess–Zumino gauge condition for an N = 2 superfield is compatible with familiar SUSY (plus U(1) gauge) transformations for the vector supermultiplet. N = 2 SUSY invariant mass and Yukawa interaction terms for the vector supermultiplet are also constructed from the superfield explicitly in addition to a free (kinetic) action.

Positioning in a flat two-dimensional space-time

The basic theory on relativistic positioning systems in a two-dimensional space-time and the analysis of the possibility of making relativistic gravimetry with these systems have been presented elsewhere [Phys. Rev. D 73 , 084017 (2006); Phys. Rev. D 74 , 104003 (2006)]. Here we summarize these results and we outline new issues on the relativistic positioning systems in Minkowski plane. We point out that the accelerations of the emitters and of the user along their trajectories are determined by the sole knowledge of the emitter positioning data and of the acceleration of only one of the emitters and only during a light echo interval.

N = 2 SUPERSYMMETRIC QED RELATED TO N = 2 VOLKOV–AKULOV MODEL

We discuss the relation between N = 2 Volkov–Akulov model and the spontaneously broken linear supersymmetry (LSUSY) interacting gauge theory for N = 2 vector and N = 2 scalar supermultiplets in two-dimensional spacetime (d = 2). The local gauge interaction of LSUSY is induced by the specific composite structure of the auxiliary fields and the consequent transformations.

On vacuum structures of [formula omitted] LSUSY QED equivalent to [formula omitted] NLSUSY model

The vacuum structure of N=2 linear supersymmetry (LSUSY) invariant QED, which is equivalent to N=2 nonlinear supersymmetry (NLSUSY) model, is studied explicitly in two-dimensional space–time (d=2). Two different isometries SO(1,3) and SO(3,1) appear for the vacuum field configuration corresponding to the various parameter regions. Two different field configurations of SO(3,1) isometry describe the two different physical vacua, i.e. one breaks spontaneously both U(1) and SUSY and the other breaks spontaneously SUSY alone.

Anomalies and Hawking radiation from the Reissner–Nordström black hole with a global monopole

We extend the work by Iso, Umetsu and Wilczek (2006 Phys. Rev. Lett. 96 151302) to derive the Hawking flux via gauge and gravitational anomalies of a most general two-dimensional non-extremal black hole spacetime with the determinant of its diagonal metric differing from unity and use it to investigate Hawking radiation from the Reissner–Nordström black hole with a global monopole by requiring the cancellation of anomalies at the horizon. It is shown that the compensating energy–momentum and gauge fluxes required to cancel gravitational and gauge anomalies at the horizon are precisely equivalent to the (1 + 1)-dimensional thermal fluxes associated with Hawking radiation emanating from the horizon at the Hawking temperature. These fluxes are universally determined by the value of anomalies at the horizon.

Polymer quantization of the CGHS model: I

We present a polymer (loop) quantization of a two-dimensional theory of dilatonic gravity known as the CGHS model. We recast the theory as a parametrized free field theory on a flat two-dimensional spacetime and quantize the resulting phase space using techniques of loop quantization. The resulting (kinematical) Hilbert space admits a unitary representation of the spacetime diffeomorphism group. We obtain the complete spectrum of the theory using a technique known as group averaging and perform quantization of Dirac observables on the resulting Hilbert space. Finally, we argue that the algebra of Dirac observables gets deformed in the quantum theory.

Implicit difference approximation for the two-dimensional space-time fractional diffusion equation

In this paper, we consider a two-dimensional fractional spacetime diffusion equation (2DFSTDE) on a finite domain. We examine an implicit difference approximation to solve the 2DFSTDE. Stability and convergence of the method are discussed. Some numerical examples are presented to show the application of the present technique.