Alternative Quantization Research Articles

Reliability of PET/CT Shape and Heterogeneity Features in Functional and Morphologic Components of Non-Small Cell Lung Cancer Tumors: A Repeatability Analysis in a Prospective Multicenter Cohort.

The main purpose of this study was to assess the reliability of shape and heterogeneity features in both the PET and the low-dose CT components of PET/CT. A secondary objective was to investigate the impact of image quantization. Methods: A Health Insurance Portability and Accountability Act-compliant secondary analysis of deidentified prospectively acquired PET/CT test-retest datasets of 74 patients from multicenter Merck and American College of Radiology Imaging Network trials was performed. Metabolically active volumes were automatically delineated on PET with a fuzzy locally adaptive bayesian algorithm. Software was used to semiautomatically delineate the anatomic volumes on the low-dose CT component. Two quantization methods were considered: a quantization into a set number of bins (quantization B) and an alternative quantization with bins of fixed width (quantization W). Four shape descriptors, 10 first-order metrics, and 26 textural features were evaluated. Bland-Altman analysis was used to quantify repeatability. Features were subsequently categorized as very reliable, reliable, moderately reliable, or poorly reliable with respect to the corresponding volume variability. Results: Repeatability was highly variable among features. Numerous metrics were identified as poorly or moderately reliable. Others were reliable or very reliable in both modalities and in all categories (shape and first-, second-, and third-order metrics). Image quantization played a major role in feature repeatability. Features were more reliable in PET with quantization B, whereas quantization W showed better results in CT. Conclusion: The test-retest repeatability of shape and heterogeneity features in PET and low-dose CT varied greatly among metrics. The level of repeatability also depended strongly on the quantization step, with different optimal choices for each modality. The repeatability of PET and low-dose CT features should be carefully considered when selecting metrics to build multiparametric models.

On the Poincaré and Gauge Symmetry of a Model where Vector and Axial Vector Interaction get Mixed up with Different Weight

A $(1+1)$ dimensional model where vector and axial vector interaction get mixed up with different weight is considered with a generalized masslike term for gauge field. Through Poincar\'e algebra it has been made confirm that only a Lorentz covariant masslike term leads to a physically sensible theory as long as the number of constraints in the phase space is two. With that admissible masslike term, phase space structure of this model with proper identification of physical canonical pair has been determined using Diracs' scheme of quantization of constrained system. The bosonized version of the model remains gauge non-invariant to start with. Therefore, with the inclusion of appropriate Wess-Zumino term it is made gauge symmetric. An alternative quantization has been carried out over this gauge symmetric version to determine the phase space structure in this situation. To establish that the Wess-Zumino fields allocates themselves in the un-physical sector of the theory an attempts has been made to get back the usual theory from the gauge symmetric theory of the extended phase-space without hampering any physical principle. It has been found that the role of gauge fixing is crucial for this transmutation.

Reformulation of boundary BF theory approach to statistical explanation of the entropy of isolated horizons

It is shown in this paper that the symplectic form for the system consisting of $D$-dimensional bulk Palatini gravity and SO$(1,1)$ BF theory on an isolated horizon as a boundary just contains the bulk term. An alternative quantization procedure for the boundary BF theory is presented. The area entropy is determined by the degree of freedom of the bulk spin network states which satisfy a suitable boundary condition. The gauge-fixing condition in the approach and the advantages of the approach are also discussed.

Towards quantum turbulence in finite temperature Bose-Einstein condensates

Motivated by the various indications that holographic superfluid is BCS like at the standard quantization but BEC like at the alternative quantization, we have implemented the alternative quantization in the dynamical holographic superfluid for the first time. With this accomplishment, we further initiate the detailed investigation of quantum turbulence in finite temperature BEC by a long time stable numerical simulation of bulk dynamics, which includes the two body decay of vortex number caused by vortex pair annihilation, the onset of superfluid turbulence signaled by Kolmogorov scaling law, and a direct energy cascade demonstrated by injecting energy to the turbulent superfluid. All of these results share the same patterns as the holographic superfluid at the standard quantization, thus suggest that these should be universal features for quantum turbulence at temperatures order of the critical temperature.

Collective excitations of massive flavor branes

We study the intersections of two sets of D-branes of different dimensionalities. This configuration is dual to a supersymmetric gauge theory with flavor hypermultiplets in the fundamental representation of the gauge group which live on the defect of the unflavored theory determined by the directions common to the two types of branes. One set of branes is dual to the color degrees of freedom, while the other set adds flavor to the system. We work in the quenched approximation, i.e., where the flavor branes are considered as probes, and focus specifically on the case in which the quarks are massive. We study the thermodynamics and the speeds of first and zero sound at zero temperature and non-vanishing chemical potential. We show that the system undergoes a quantum phase transition when the chemical potential approaches its minimal value and we obtain the corresponding non-relativistic critical exponents that characterize its critical behavior. In the case of (2+1)-dimensional intersections, we further study alternative quantization and the zero sound of the resulting anyonic fluid. We finally extend these results to non-zero temperature and magnetic field and compute the diffusion constant in the hydrodynamic regime. The numerical results we find match the predictions by the Einstein relation.

Holographic anyonization: a systematic approach

Anyons have garnered substantial interest theoretically as well as experimentally. Due to the intricate nature of their interactions, however, even basic notions such as the equation of state for any kind of anyon gas have eluded a profound understanding so far. Using holography as a guiding principle, we propose a general method for an alternative quantization of electromagnetic degrees of freedom in the gravitational dual to obtain an effective physical description of strongly correlated anyonic systems. We then demonstrate the application of this prescription in a toy model of an anyonic fluid at finite charge density and magnetic field, dual to a dyonic black brane in AdS_4, and compute the equation of state and various transport coefficients explicitly.

Pointwise Reconstruction of Wave Functions from Their Moments through Weighted Polynomial Expansions: An Alternative Global-Local Quantization Procedure

Many quantum systems admit an explicit analytic Fourier space expansion, besides the usual analytic Schrödinger configuration space representation. We argue that the use of weighted orthonormal polynomial expansions for the physical states (generated through the power moments) can define an L2 convergent, non-orthonormal, basis expansion with sufficient pointwise convergent behaviors, enabling the direct coupling of the global (power moments) and local (Taylor series) expansions in configuration space. Our formulation is elaborated within the orthogonal polynomial projection quantization (OPPQ) configuration space representation previously developed The quantization approach pursued here defines an alternative strategy emphasizing the relevance of OPPQ to the reconstruction of the local structure of the physical states.

A strongly coupled anyon material

We use alternative quantisation of the D3-D5 system to explore properties of a strongly coupled anyon material at finite density and temperature. We study the transport properties of the material and find both diffusion and massive holographic zero sound modes. By studying the anyon number conductivity we also find evidence for the anyonic analogue of the metal-insulator transition.

Quantizations of probability measures and preservation of the convex order

Two probability measures admit a martingale transition if and only if they are ordered in the convex order (Kellerer, 1972). We show that the commonly used quantization method, L2-quantization, does not have the property of preserving the convex order. We introduce an alternative quantization method and demonstrate that it preserves the convex order. This result has implications concerning the choice of quantization methods for the numerical construction of martingales with specified marginals.

Stochastic variational method as quantization scheme: Field quantization of the complex Klein–Gordon equation

Stochastic Variational Method (SVM) is the generalization of the variation method to the case with stochastic variables. In the series of papers, we investigate the applicability of SVM as an alternative field quantization scheme. Here, we discuss the complex Klein-Gordon equation. In this scheme, the Euler-Lagrangian equation for the stochastic fields leads to the functional Schroedinger equation, which in turn can be interpreted as the ideal fluid equation in the functional space. We show that the Fock state vector is given by the stationary solution of these differential equations and various results in the usual canonical quantization can be reproduced, including the effect of anti-particles. The present formulation is a quantization scheme based on commutable variables, so that there appears no ambiguity associated with the ordering of operators, for example, in the definition of Noether charges.

Universal properties of cold holographic matter

We study the collective excitations of holographic quantum liquids formed in the low energy theory living at the intersection of two sets of D-branes. The corresponding field theory dual is a supersymmetric Yang-Mills theory with massless matter hypermultiplets in the fundamental representation of the gauge group which generically live on a defect of the unflavored theory. Working in the quenched (probe) approximation, we focus on determining the universal properties of these systems. We analyze their thermodynamics, the speed of first sound, the diffusion constant, and the speed of zero sound. We study the influence of temperature, chemical potential, and magnetic field on these quantities, as well as on the corresponding collisionless/hydrodynamic crossover. We also generalize the alternative quantization for all conformally ${\mathrm{AdS}}_{4}$ cases and study the anyonic correlators.

Quantum black holes in loop quantum gravity

We study the quantization of spherically symmetric vacuum spacetimes within loop quantum gravity. In particular, we give additional details about our previous work in which we showed that one could complete the quantization of the model and that the singularity inside black holes is resolved. Moreover, we consider an alternative quantization based on a slightly different kinematical Hilbert space. The ambiguity in kinematical spaces stems from how one treats the periodicity of one of the classical variables in these models. The corresponding physical Hilbert spaces solve the diffeomorphism and Hamiltonian constraint but their intrinsic structure is radically different depending on the kinematical Hilbert space one started from. In both cases there are quantum observables that do not have a classical counterpart. However, one can show that at the end of the day, by examining Dirac observables, both quantizations lead to the same physical predictions.

Holographic plasma and anyonic fluids

We use alternative quantisation of the $D3/D5$ system to explore properties of a strongly coupled charged plasma and strongly coupled anyonic fluids. The $S$-transform of the $D3/D5$ system is used as a model for charged matter interacting with a U(1) gauge field in the large coupling regime, and we compute the dispersion relationship of the propagating electromagnetic modes as the density and temperature are changed. A more general $SL(2,\mathbb{Z})$ transformation gives a strongly interacting anyonic fluid, and we study its transport properties as we change the statistics of the anyons and the background magnetic field.

Born–Jordan quantization and the uncertainty principle

The Weyl correspondence and the related Wigner formalism lie at the core of traditional quantum mechanics. We discuss here an alternative quantization scheme, the idea of which goes back to Born and Jordan, and which has recently been revived in another context, namely time–frequency analysis. We show in particular that the uncertainty principle does not enjoy full symplectic covariance properties in the Born and Jordan scheme, as opposed to what happens in the Weyl quantization.

Holographic anyonic superfluidity

Starting with a holographic construction for a fractional quantum Hall state based on the D3-D7' system, we explore alternative quantization conditions for the bulk gauge fields. This gives a description of a quantum Hall state with various filling fractions. For a particular alternative quantization of the bulk gauge fields, we obtain a holographic anyon fluid in a vanishing background magnetic field. We show that this system is a superfluid, exhibiting the relevant gapless excitation.

High energy modifications of blackbody radiation and dimensional reduction

Quantization prescriptions that realize generalized uncertainty relations (GUP) are motivated by quantum gravity arguments that incorporate a fundamental length scale. We apply two such methods, polymer and deformed Heisenberg quantization, to scalar field theory in Fourier space. These alternative quantizations modify the oscillator spectrum for each mode, which in turn affects the blackbody distribution. We find that for a large class of modifications, the equation of state relating pressure $P$ and energy density $\rho$ interpolates between $P=\rho/3$ at low $T$ and $P=2\rho/3$ at high $T$, where $T$ is the temperature. Furthermore, the Stefan-Boltzman law gets modified from $\rho \propto T^{4}$ to $\rho \propto T^{5/2}$ at high temperature. This suggests an effective reduction to 2.5 spacetime dimensions at high energy.

Time-Symmetric Quantization in Spacetimes with Event Horizons

The standard quantization formalism in spacetimes with event horizons implies a non-unitary evolution of quantum states, as initial pure states may evolve into thermal states. This phenomenon is behind the famous black hole information loss paradox which provoked long-standing debates on the compatibility of quantum mechanics and gravity. In this paper we demonstrate that within an alternative time-symmetric quantization formalism thermal radiation is absent and states evolve unitarily in spacetimes with event horizons. We also discuss the theoretical consistency of the proposed formalism. We explicitly demonstrate that the theory preserves the microcausality condition and suggest a “reinterpretation postulate” to resolve other apparent pathologies associated with negative energy states. Accordingly as there is a consistent alternative, we argue that choosing to use time-asymmetric quantization is a necessary condition for the black hole information loss paradox.

The Unruh Effect in General Boundary Quantum Field Theory

In the framework of the general boundary formulation (GBF) of scalar quantum field theory we obtain a coincidence of expectation values of local observables in the Minkowski vacuum and in a particular state in Rindler space. This coincidence could be seen as a consequence of the identification of the Minkowski vacuum as a thermal state in Rindler space usually associated with the Unruh effect. However, we underline the difficulty in making this identification in the GBF. Beside the Feynman quantization prescription for observables that we use to derive the coincidence of expectation values, we investigate an alternative quantization prescription called Berezin-Toeplitz quantization prescription, and we find that the coincidence of expectation values does not exist for the latter.

Enhanced quantization: a primer

Although classical mechanics and quantum mechanics are separate disciplines, we live in a world where Planck’s constant ℏ > 0, meaning that the classical and quantum world views must actually coexist. Traditionally, canonical quantization procedures postulate a direct linking of various c-number and q-number quantities that lie in disjoint realms, along with the quite distinct interpretations given to each realm. In this paper we propose a different association of classical and quantum quantities that renders classical theory a natural subset of quantum theory letting them coexist as required. This proposal also shines light on alternative linking assignments of classical and quantum quantities that offer different perspectives on the very meaning of quantization. In this paper we focus on elaborating the general principles, while elsewhere we have published several examples of what this alternative viewpoint can achieve; these examples include removal of singularities in classical solutions to certain models, and an alternative quantization of several field theory models that are trivial when quantized by traditional methods but become well defined and nontrivial when viewed from the new viewpoint.

Time discretization and quantization methods for optimal multiple switching problem

In this paper, we study probabilistic numerical methods based on optimal quantization algorithms for computing the solution to optimal multiple switching problems with regime-dependent state process. We first consider a discrete-time approximation of the optimal switching problem, and analyse its rate of convergence. Given a time step h, the error is in general of order (hlog(1/h))1/2, and of order h1/2 when the switching costs do not depend on the state process. We next propose quantization numerical schemes for the space discretization of the discrete-time Euler state process. A Markovian quantization approach relying on the optimal quantization of the normal distribution arising in the Euler scheme is analysed. In the particular case of uncontrolled state process, we describe an alternative marginal quantization method, which extends the recursive algorithm for optimal stopping problems as in Bally (2003) [1]. A priori Lp-error estimates are stated in terms of quantization errors. Finally, some numerical tests are performed for an optimal switching problem with two regimes.