scholarly journals New Affine Coherent States Based on Elements of Nonrenormalizable Scalar Field Models

2010 ◽  
Vol 2010 ◽  
pp. 1-16 ◽  
Author(s):  
John R. Klauder
Keyword(s):  
Scalar Field ◽  
Ground State ◽  
Coherent States ◽  
Continuum Limit ◽  
Quantum Fields ◽  
Commutation Relations ◽  
Scalar Field Models ◽  
Scalar Quantum ◽  
Definition Of ◽  
The Continuum

Recent proposals for a nontrivial quantization of covariant, nonrenormalizable, self-interacting, scalar quantum fields have emphasized the importance of quantum fields that obey affine commutation relations rather than canonical commutation relations. When formulated on a spacetime lattice, such models have a lattice version of the associated ground state, and this vector is used as the fiducial vector for the definition of the associated affine coherent states, thus ensuring that in the continuum limit, the affine field operators are compatible with the system Hamiltonian. In this article, we define and analyze the associated affine coherent states as well as briefly review the author's approach to nontrivial formulations of such nonrenormalizable models.

scholarly journals Ground-state energy of a Richardson-Gaudin integrable BCS model

2020 ◽  
Vol 2 (1) ◽  
Author(s):  
Yibing Shen ◽  
Phillip Isaac ◽  
Jon Links
Keyword(s):  
Integral Equation ◽  
Ground State Energy ◽  
Ground State ◽  
Continuum Limit ◽  
State Energy ◽  
Mean Field ◽  
Bcs Model ◽  
Energy Expression ◽  
The Continuum

We investigate the ground-state energy of a Richardson-Gaudin integrable BCS model, generalizing the closed and open p+ip models. The Hamiltonian supports a family of mutually commuting conserved operators satisfying quadratic relations. From the eigenvalues of the conserved operators we derive, in the continuum limit, an integral equation for which a solution corresponding to the ground state is established. The energy expression from this solution agrees with the BCS mean-field result.

scholarly journals Topological susceptibility with a single light quark flavour

2018 ◽  
Vol 175 ◽  
pp. 14017 ◽  
Author(s):  
Julien Frison ◽  
Ryuichiro Kitano ◽  
Norikazu Yamada
Keyword(s):  
Quark Mass ◽  
Continuum Limit ◽  
Light Quark ◽  
The Other ◽  
Theoretical Argument ◽  
Up Quark ◽  
Order Of Magnitude ◽  
Quark Flavour ◽  
Definition Of ◽  
The Continuum

One of the historical suggestions to tackle the strong CP problem is to take the up quark mass to zero while keeping md finite. The θ angle is then supposed to become irrelevant, i.e. the topological susceptibility vanishes. However, the definition of the quark mass is scheme-dependent and identifying the mu = 0 point is not trivial, in particular with Wilson-like fermions. More specifically, up to our knowledge there is no theoretical argument guaranteeing that the topological susceptibility exactly vanishes when the PCAC mass does. We will present our recent progresses on the empirical check of this property using Nf = 1 + 2 flavours of clover fermions, where the lightest fermion is tuned very close to [see formula in PDF] and the mass of the other two is kept of the order of magnitude of the physical ms. This choice is indeed expected to amplify any unknown non-perturbative effect caused by mu ≠ md. The simulation is repeated for several βs and those results, although preliminary, give a hint about what happens in the continuum limit.

A NEW DEFINITION OF BOSONS

1999 ◽  
Vol 13 (24n25) ◽  
pp. 2909-2913 ◽  
Author(s):  
ENRICO CELEGHINI
Keyword(s):  
Group Theory ◽  
Hopf Algebra ◽  
Coherent States ◽  
Continuum Limit ◽  
Black Body ◽  
Black Body Radiation ◽  
Bose Condensation ◽  
Experimental Results ◽  
Text Representation ◽  
Definition Of

A recipe is given to reproduce algebraically the Bose prescription in Quantum Statistics. Bosons are thus defined as coherent states of the [Formula: see text] representation of the Lie-Hopf algebra su(1, 1), while h(1) is shown to be related to Boltzmann statistics. The technical power of group theory is used to show that black-body radiation formula as well as all other experimental results obtained in continuum limit do not require Bose distribution but are compatible with many other less symmetric ones. This may have dramatical effects on the predictions on Bose condensation.

THE CHIRAL U(1) SYMMETRY IN LATTICE QCD WITH WILSON FERMIONS

1995 ◽  
Vol 10 (15) ◽  
pp. 2269-2290 ◽  
Author(s):  
CARLO UNGARELLI
Keyword(s):  
Lattice Qcd ◽  
Chiral Symmetry ◽  
Continuum Limit ◽  
Axial Current ◽  
Numerical Results ◽  
Ward Identities ◽  
Definition Of ◽  
The Continuum ◽  
Wilson Fermions

The properties of singlet flavor chiral symmetry of lattice QCD with Wilson fermions are analyzed. We show that a suitable U(1) axial current can be defined, satisfying, in the continuum limit, the Adler-Bell-Jackiw anomaly. Moreover, the renormalization properties of composite operators which appear in U(1) chiral Ward identities are discussed. Finally, starting from the renormalized Ward identities for the axial U(1) current, we analyze a definition of topological susceptibility suitable for nonperturbative studies and discuss preliminary numerical results.

scholarly journals DISCRETE GRAVITY AND ITS CONTINUUM LIMIT

2005 ◽  
Vol 20 (03) ◽  
pp. 213-225
Author(s):  
YI LING
Keyword(s):  
Scalar Field ◽  
Cosmological Constant ◽  
Continuum Limit ◽  
Constant Term ◽  
Chaplygin Gas ◽  
Fine Tuning ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Cosmological Singularity ◽  
The Continuum

Recently Gambini and Pullin proposed a new consistent discrete approach to quantum gravity and applied it to cosmological models. One remarkable result of this approach is that the cosmological singularity can be avoided in a general fashion. However, whether the continuum limit of such discretized theories exists is model dependent. In the case of massless scalar field coupled to gravity with Λ=0, the continuum limit can only be achieved by fine tuning the recurrence constant. We regard this failure as the implication that cosmological constant should vary with time. For this reason we replace the massless scalar field by Chaplygin gas which may contribute an effective cosmological constant term with the evolution of the universe. It turns out that the continuum limit can indeed be reached in this case.

ON THE DIMERIZATION OF LINEAR POLYMERS

1989 ◽  
Vol 03 (02) ◽  
pp. 125-133 ◽  
Author(s):  
C. ARAGÃO DE CARVALHO
Keyword(s):  
Free Energy ◽  
Effective Potential ◽  
Ground State ◽  
Finite Temperature ◽  
Continuum Limit ◽  
Linear Polymers ◽  
Renormalization Condition ◽  
Loop Approximation ◽  
The One ◽  
The Continuum

We use the continuum limit of the Su-Schrieffer-Heeger model for linear polymers to construct its effective potential (Gibbs free energy) both at zero and finite temperature. We study both trans and cis-polymers. Our results show that, depending on a renormalization condition to be extracted from experiment, there are several possibilities for the minima of the dimerized ground state of cis-polymers. All calculations are done in the one-loop approximation.

scholarly journals GROUND STATE OF THE MASSLESS NELSON MODEL WITHOUT INFRARED CUTOFF IN A NON-FOCK REPRESENTATION

2001 ◽  
Vol 13 (09) ◽  
pp. 1075-1094 ◽  
Author(s):  
ASAO ARAI
Keyword(s):  
Scalar Field ◽  
Ground State ◽  
Coupling Constant ◽  
Fock Representation ◽  
Nelson Model ◽  
Canonical Commutation Relations ◽  
Commutation Relations ◽  
Quantum Particles ◽  
Infrared Cutoff ◽  
Massless Quantum

We consider a model of quantum particles coupled to a massless quantum scalar field, called the massless Nelson model, in a non-Fock representation of the time-zero fields which satisfy the canonical commutation relations. We show that the model has a ground state for all values of the coupling constant even in the case where no infrared cutoff is made. The non-Fock representation used is inequivalent to the Fock one if no infrared cutoff is made.

scholarly journals High-precision evaluation of the vibrational spectra of long-range molecules

2001 ◽  
Vol 79 (2-3) ◽  
pp. 109-119
Author(s):  
C Tannous ◽  
J Langlois
Keyword(s):  
Long Range ◽  
Vibrational Spectra ◽  
Ground State ◽  
Function Method ◽  
Continuum Limit ◽  
Energy Levels ◽  
Electronic States ◽  
Canonical Function ◽  
Precision Evaluation ◽  
The Continuum

Vibrational spectra of long-range molecules are determined accurately and to arbitrary accuracy with the Canonical Function Method. The energy levels of the 0–g and 1u electronic states of the 23Na2 molecule are determined from the ground state up to the continuum limit. The method is validated by comparison with previous results obtained for different potentials adapted to long-range molecules. PACS Nos.: 03.65-w, 31.15Gy, 33.20.Tp

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