Vacuum Wave Function Research Articles

A Realistic Interpretation of Quantum Wavefunctions as Temperature Dependent Vacuum Polarization Waves

We discuss in this paper a novel interpretation of Born rule as an approximated thermodynamic law which emerges from the interaction of a quantum system with a non-stationary thermal bath associated to vacuum fluctuations induced by external environment radiation. In particular we assume that vacuum polarization is a real non relativistic phenomena caused by hidden vacuum charge oscillations which diffuses heat energy in a dispersive and dissipative dielectric medium with a temperature dependent speed of propagation. We propose a model which couples vacuum wavefunctions to vacuum charge fluctuations and we deduce a temperature dependent running fine structure constant function proportional, at first approximation, to the squared of the effective electron charge and compatible with known experimental data. We interpret the vacuum symmetry breaking energy fluctuations induced in scattering experiments of particle physics and in laser assisted nuclear reactions as thermal quasi-monochromatic beams produced by the decay of hidden non equilibrium massive photons propagating with a variable light speed. We suggest, exploiting an old analogy between plasmons and pseudo Goldstone bosons, to interpret heat diffusion of this non relativistic polarized vacuum as a real De Broglie electromagnetic scalar wave associated to the radiation emitted by the hidden massive photons with acceleration proportional to vacuum Unruh like temperature. We predict a temperature dependent deviation from Coulomb law and a generalized dispersive law of these hidden unstable photons that could be revealed as not stationary coloured noise in experiments on anomalous heat diffusions associated to the decay of unstable accelerated pairs produced in nuclear physics experiments. We discuss then how our proposal of a temperature dependent non relativistic vacuum polarization might be applied to deduce a dynamic generalization of Born rule based on a realistic interpretation of quantum wavefunctions as averaged electromagnetic waves of hidden massive photons. Finally we suggest to test our time asymmetric model looking for very fast oscillating polarization thermal waves emitted during the not instantaneous wavefunction collapse and revealed as not stationary bulk heating effects in experiments on accelerated conductors and nanoconductors.

Light-cone distribution amplitudes of the nucleon and \u2206 baryon

We investigate the light-cone wave functions and leading-twist distribution amplitudes for the nucleon and ∆ baryon within the framework of the chiral quark-soliton model. The baryon wave function consists of the valence quark and vacuum wave functions. The vacuum wave functions generate all possible higher Fock states by expanding them. We find that it is essential to consider the five-quark component and relativistic corrections to evaluate the distribution amplitudes of the nucleon and ∆ isobar. Having taken into account them, we derive the distribution amplitudes. The results are in good agreement with the lattice data.

Improved variational approach to QCD in Coulomb gauge

The variational approach to QCD in Coulomb gauge developed previously by the T\"ubingen group is improved by enlarging the space of the quark trial vacuum wave functionals through a new Dirac structure in the quark-gluon coupling. Our Ansatz for the quark vacuum wave functional ensures that all linear divergences cancel in the quark gap equation resulting from the minimization of the energy calculated to two-loop order. The logarithmic divergences are absorbed in a renormalized coupling which is adjusted to reproduce the phenomenological value of the quark condensate. We also unquench the gluon propagator and show that the unquenching effects are generally small and amount to a small reduction in the midmomentum regime.

The Hamiltonian Approach to Yang-Mills (2+1): An Update and Corrections to String Tension

Yang-Mills theories in 2+1 (or 3) dimensions are interesting as nontrivial gauge theories in their own right and as effective theories of QCD at high temperatures. I shall review the basics of our Hamiltonian approach to this theory, emphasizing symmetries with a short update on its status. We will show that the calculation of the vacuum wave function for Yang-Mills theory in 2+1 dimensions is in the lowest order of a systematic expansion. Expectation values of observables can be calculated using an effective interacting chiral boson theory, which also leads to a natural expansion as a double series in the coupling constant (to be interpreted within a resummed perturbation series) and a particular kinematical factor. The calculation of the first set of corrections in this expansion shows that the string tension is modified by about −0.3% to −2.8% compared to the lowest order value. This is in good agreement with lattice estimates.

Dynamical Quarkonia Suppression from Complex Potentials

I address the effect that a temperature dependent potential has on the suppression of heavy quarkonia states in deconfined hadronic matter. I focus on a simple medium: a homogenous, fixed temperature and deconfined system with a finite lifetime (QGP-brick). Assuming that all the interactions of a heavy quark anti-quark (Q – Q̄) pair with the medium can be recast into an in-medium potential, I solve the time dependent Schrödinger equation to evolve the density matrix which describes the hard pair production and its connection to the final distribution of hadrons after the medium disappears. For those temperatures in which bound states survive in the medium, I find a non-trivial dependence of the production of excited quarkonia states on the in-medium levels, due to the mixing of vacuum and in-medium wave functions. This mixing leads, in particular, to the enhancement of the relative abundance of 2S to 1S states for the case in which the in-medium ground state of the Q – Q̄ system is dissolved.

Dynamical quarkonia suppression in a QGP-brick

I address the effect that a temperature dependent potential has on the suppression of heavy quarkonia states in deconfined hadronic matter. I focus on a simple medium: a homogenous, fixed temperature and deconfined system with a finite lifetime (QGP-brick). Assuming that all the interactions of a heavy quark anti-quark ($Q-\bar Q$) pair with the medium can be recast into an in-medium potential, I solve the time dependent Schr\"odinger equation to evolve the density matrix which describes the hard pair production and its connection to the final distribution of hadrons after the medium disappears. For those temperatures in which bound states survive in the medium, I find a non-trivial dependence of the production of excited quarkonia states on the in-medium levels, due to the mixing of vacuum and in-medium wave functions. This mixing leads, in particular, to the enhancement of the relative abundance of 2S to 1S states for those systems in which the in-medium ground state of the $Q-\bar Q$ system is dissolved or close to threshold. I also explore quarkonia production in a non-homogeneous expanding medium and find that the finite formation time effects arising from the low binding energies of in-medium states lead to the insensitivity of the heavy mesons yield to the hottest part of the system evolution.

Testing proposals for the Yang-Mills vacuum wavefunctional by measurement of the vacuum

We review a method, suggested many years ago, to numerically measure the relative amplitudes of the true Yang-Mills vacuum wavefunctional in a finite set of lattice-regulated field configurations. The technique is applied in 2+1 dimensions to sets of abelian plane wave configurations of varying amplitude and wavelength, and sets of non-abelian constant configurations. The results are compared to the predictions of several proposed versions of the Yang-Mills vacuum wavefunctional that have appeared in the literature. These include (i) a suggestion in temporal gauge due to Greensite and Olejnik; (ii) the "new variables" wavefunction put forward by Karabali, Kim, and Nair; (iii) a hybrid proposal combining features of the temporal gauge and new variables wavefunctionals; and (iv) Coulomb gauge wavefunctionals developed by Reinhardt and co-workers, and by Szczepaniak and co-workers. We find that wavefunctionals which simplify to a "dimensional reduction" form at large scales, i.e. which have the form of a probability distribution for two-dimensional lattice gauge theory, when evaluated on long-wavelength configurations, have the optimal agreement with the data.

On the perturbative stability of quantum field theories in de Sitter space

We use a field theoretic generalization of the Wigner-Weisskopf method to study the stability of the Bunch-Davies vacuum state for a massless, conformally coupled interacting test field in de Sitter space. We find that in $\lambda \phi^4$ theory the vacuum does {\em not} decay, while in non-conformally invariant models, the vacuum decays as a consequence of a vacuum wave function renormalization that depends \emph{singularly} on (conformal) time and is proportional to the spatial volume. In a particular regularization scheme the vacuum wave function renormalization is the same as in Minkowski spacetime, but in terms of the \emph{physical volume}, which leads to an interpretation of the decay. A simple example of the impact of vacuum decay upon a non-gaussian correlation is discussed. Single particle excitations also decay into two particle states, leading to particle production that hastens the exiting of modes from the de Sitter horizon resulting in the production of \emph{entangled superhorizon pairs} with a population consistent with unitary evolution. We find a non-perturbative, self-consistent "screening" mechanism that shuts off vacuum decay asymptotically, leading to a stationary vacuum state in a manner not unlike the approach to a fixed point in the space of states.

Non-Gaussian wave functionals in Coulomb gauge Yang-Mills theory

A general method to treat non-Gaussian vacuum wave functionals in the Hamiltonian formulation of a quantum field theory is presented. By means of Dyson--Schwinger techniques, the static Green functions are expressed in terms of the kernels arising in the Taylor expansion of the exponent of the vacuum wave functional. These kernels are then determined by minimizing the vacuum expectation value of the Hamiltonian. The method is applied to Yang--Mills theory in Coulomb gauge, using a vacuum wave functional whose exponent contains up to quartic terms in the gauge field. An estimate of the cubic and quartic interaction kernels is given using as input the gluon and ghost propagators found with a Gaussian wave functional.

Theta-vacuum and large N limit in [formula omitted]σ models

The θ dependence of the vacuum energy density in C P N − 1 models is re-analysed in the semiclassical approach, the 1 / N expansion and arguments based on the nodal structure of vacuum wavefunctionals. The 1 / N expansion is shown not to be in contradiction with instanton physics at finite (spacetime) volume V. The interplay of large volume V and large N parameter gives rise to two regimes with different θ dependence, one behaving as a dilute instanton gas and the other dominated by the traditional large N picture, where instantons reappear as resonances of the one-loop effective action, even in the absence of regular instantonic solutions. The realms of the two regimes are given in terms of the mass gap m by m 2 V ≪ N and m 2 V ≫ N , respectively. The small volume regime m 2 V ≪ N is relevant for physical effects associated to the physics of the boundary, like the leading rôle of edge states in the quantum Hall effect, which, however, do not play any rôle in the thermodynamic limit at large N. Depending on the order in which the limits N → ∞ and V → ∞ are taken, two different theories are obtained; this is the hallmark of a phase transition at 1 / N = 0 .

The Hamiltonian approach to Yang–Mills [formula omitted]: Expansion scheme and corrections to string tension

We carry out further analysis of the Hamiltonian approach to Yang–Mills theory in 2 + 1 dimensions which helps to place the calculation of the vacuum wave function and the string tension in the context of a systematic expansion scheme. The solution of the Schrödinger equation is carried out recursively. The computation of correlators is re-expressed in terms of a two-dimensional chiral boson theory. The effective action for this theory is calculated to first order in our expansion scheme and to the fourth order in a kinematic expansion parameter. The resulting corrections to the string tension are shown to be very small, in the range −0.3% to −2.8%, moving our prediction closer to the recent lattice estimates.

Robustness of the vacuum wave function and other matters for Yang-Mills theory

In the first part of this paper, we present a set of simple arguments to show that the two-dimensional gauge anomaly and the ($2+1$)-dimensional Lorentz symmetry determine the leading Gaussian term in the vacuum wave function of ($2+1$)-dimensional Yang-Mills theory. This is to highlight the robustness of the wave function and its relative insensitivity to the choice of regularizations. We then comment on the correspondence with the explicit calculations done in earlier papers. We also make some comments on the nature of the gauge-invariant configuration space for Euclidean three-dimensional gauge fields (relevant to ($3+1$)-dimensional Yang-Mills theory).

Approximated seventh order calculation of the vacuum wave function of2+1dimensional SU(2) lattice gauge theory

Using the coupled cluster expansion with the random phase approximation, we calculate the long wavelength vacuum wave function and the vacuum state energy of $2+1$ dimensional Hamiltonian SU(2) lattice gauge theory up to the seventh order. The coefficients ${\ensuremath{\mu}}_{0}$, ${\ensuremath{\mu}}_{2}$ of the vacuum wave function show good scaling behavior and convergence in high order calculations.

Flat spacetime vacuum in loop quantum gravity

We propose a state in loop quantum gravity theory with zero cosmological constant such that it could be associated with the flat spacetime vacuum solution. This state is constructed by defining the loop transform coefficients of a flat connection wavefunction in the holomorphic representation which satisfies all the constraints of quantum general relativity and it is peaked around the flat space triads. The loop transform coefficients are defined as spin-foam state sum invariants of the spin networks embedded in the spatial manifold for the SU(2) quantum group. We also obtain an expression for the vacuum wavefunction in the triad representation, by defining the corresponding spin network functional integrals as SU(2) quantum group state sums.

Density matrix renormalization group in a two-dimensional 4Hamiltonian lattice model

Density matrix renormalization group (DMRG) is applied to a (1+1)-dimensional $\lambda\phi^4$ model. Spontaneous breakdown of discrete $Z_2$ symmetry is studied numerically using vacuum wavefunctions. We obtain the critical coupling $(\lambda/\mu^2)_{\rm c}=59.89\pm 0.01$ and the critical exponent $\beta=0.1264\pm 0.0073$, which are consistent with the Monte Carlo and the exact results, respectively. The results are based on extrapolation to the continuum limit with lattice sizes $L=250,500$, and 1000. We show that the lattice size L=500 is sufficiently close to the the limit $L\to\infty$.

Yang-Mills theory, 2 + 1 and 3 + 1 dimensions

I review the analysis of (2+1)-dimensional Yang-Mills (YM2+1) theory via the use of gauge-invariant matrix variables. The vacuum wavefunction, string tension, the propagator mass for gluons, its relation to the magnetic mass for YM3+1at nonzero temperature and the extension of our analysis to the Yang-Mills-Chern-Simons theory are discussed. A possible extension to 3 + 1 dimensions is also briefly considered.

Improved lattice gauge field Hamiltonian: The three-dimensional case

Using the improved lattice gauge field Hamiltonian and the truncated eigenvalue equation method, we compute the vacuum wave function and mass gap of three-dimensional SU(2) gauge field theory. Our results show that the improved theory leads to a significant reduction of violation of scaling, that is, using the improved lattice gauge field Hamiltonian, the calculations can be carried out up to a much weaker coupling region than using the unimproved one, with good scaling behavior.

D-branes in topological membranes

It is shown how two-dimensional states corresponding to D-branes arise in orbifolds of topologically massive gauge and gravity theories. Brane vertex operators naturally appear in induced worldsheet actions when the three-dimensional gauge theory is minimally coupled to external charged matter and the orbifold relations are carefully taken into account. Boundary states corresponding to D-branes are given by vacuum wavefunctionals of the gauge theory in the presence of the matter, and their various constraints, such as the Cardy condition, are shown to arise through compatibility relations between the orbifold charges and bulk gauge invariance. We show that with a further conformally-invariant coupling to a dynamical massless scalar field theory in three dimensions, the brane tension is naturally set by the bulk mass scales and arises through dynamical mechanisms. As an auxilliary result, we show how to describe string descendent states in the three-dimensional theory through the construction of gauge-invariant excited wavefunctionals.

Bosonic vacuum wave functions from the BCS-type wave function of the ground state of the massless Thirring model

A BCS-type wave function describes the ground state of the massless Thirring model in the chirally broken phase. The massless Thirring model with fermion fields quantized in the chirally broken phase bosonizes to the quantum field theory of the free massless (pseudo)scalar field [Eur. Phys. J. C 20 (2001) 723]. The wave functions of the ground state of the free massless (pseudo)scalar field are obtained from the BCS-type wave function by averaging over quantum fluctuations of the Thirring fermion fields. We show that these wave functions are orthogonal, normalized and non-invariant under shifts of the massless (pseudo)scalar field. This testifies the spontaneous breaking of the field-shift symmetry in the quantum field theory of a free massless (pseudo)scalar field. We show that the vacuum-to-vacuum transition amplitude calculated for the bosonized BCS-type wave functions coincides with the generating functional of Green functions defined only by the contribution of vibrational modes [Eur. Phys. J. C 24 (2002) 653]. This confirms the assumption that the bosonized BCS-type wave function is defined by the collective zero-mode [hep-th/0212226]. We argue that the obtained result is not a counterexample to the Mermin–Wagner–Hohenberg and Coleman theorems.

The Discrete KP and KdV Equations over Finite Fields

We propose an algebro-geometric method for constructing solutions of the discrete KP equation over a finite field. We also perform the corresponding reduction to the finite-field version of the discrete KdV equation. We write formulas that allow constructing multisoliton solutions of the equations starting from vacuum wave functions on an arbitrary nonsingular curve.