scholarly journals Revisiting on-shell renormalization conditions in theories with flavor mixing

2016 ◽  
Vol 31 (24) ◽  
pp. 1630038 ◽  
Author(s):  
W. Grimus ◽  
M. Löschner
Keyword(s):  
Canonical Form ◽  
Majorana Fermions ◽  
Pole Mass ◽  
Full Agreement ◽  
Parity Conservation ◽  
Flavor Mixing ◽  
Fermionic Fields

In this review, we present a derivation of the on-shell renormalization conditions for scalar and fermionic fields in theories with and without parity conservation. We also discuss the specifics of Majorana fermions. Our approach only assumes a canonical form for the renormalized propagators and exploits the fact that the inverse propagators are nonsingular in [Formula: see text], where [Formula: see text] is the external four-momentum and [Formula: see text] is a pole mass. In this way, we obtain full agreement with commonly used on-shell conditions. We also discuss how they are implemented in renormalization.

Studies Regarding the Architectural Design of Various Composites and Nanofibres Used in Dental Medicine

2018 ◽  
Vol 69 (2) ◽  
pp. 328-331
Author(s):  
Irina Gradinaru ◽  
Leonard Ignat ◽  
Cristina Gena Dascalu ◽  
Laurentiu Valentin Soroaga ◽  
Magda Ecaterina Antohe
Keyword(s):  
Composite Structures ◽  
Architectural Design ◽  
Dental Restoration ◽  
Fibrillar Structure ◽  
Fiber Post ◽  
Fiber Glass ◽  
Full Agreement ◽  
Sem Images ◽  
Structural Modifications ◽  
New Formulation

The aim of this study was represented by the definition and testing of a new formulation strategy and the functionality of composite materials, while ensuring the optimization of the relevant properties for the dental restoration processes through the use of precise techniques of characterization, the modification and functionality of the components in view of obtaining results that are characterized by an optimum biomechanical and bioactive relation, in full agreement with the particularities of the dental structure that requires restoration. In view of obtaining new resistant composite structures we made a number of 10 samples including extracted teeth with various losses of dental substance and the structural modifications included 3 types of composites, whose structure was improved by the introduction of inorganic fillings based on hydroxyapatite and silver nanoparticles. All these structures were reinforced with two types of fibers, Reforpost fiber glass kit (Angelus) and Fiber post Schulzer Pre-silanized; With regard to the use of composite structures improved by HA addition, we notice a slight lacunary structure on the SEM images due to the properties of HA, an aspect present at much smaller dimensions in the silver � HA mix. The size of the grains associated with their continuous uniformity and adherence for the fibrillar structure stands out at the samples with hydroxyapatite, the first place as uniformity and adherence going to the composite of the nanofiller technology category.

The canonical form of invariant matrices

1970 ◽  
Vol 68 (1) ◽  
pp. 21-25 ◽  
Author(s):  
D. B. Hunter
Keyword(s):  
Canonical Form ◽  
General Matrix ◽  
Invariant Matrices

1. Introduction. Let A[λ] be the irreducible invariant matrix of a general matrix of order n × n, corresponding to a partition (λ) = (λ1, λ2, …, λr) of some integer m. The problem to be discussed here is that of determining the canonical form of A[λ] when that of A is known.

Particle and Astro-physics Challenge Kant’s Phenomenolism

1998 ◽  
pp. 323-333
Author(s):  
Lawrence H. Starkey
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Physical Basis ◽  
Primary Sources ◽  
One Dimension ◽  
Space Curves ◽  
Slowing Down ◽  
Parity Conservation ◽  
Charge Parity ◽  
Einstein’S General Relativity

For two centuries Kant's first Critique has nourished various turns against transcendent metaphysics and realism. Kant was scandalized by reason's impotence in confronting infinity (or finitude) as seen in the divisibility of particles and in spatial extension and time. Therefore, he had to regard the latter as subjective and reality as imponderable. In what follows, I review various efforts to rationalize Kant's antinomies-efforts that could only flounder before the rise of Einstein's general relativity and Hawking's blackhole cosmology. Both have undercut the entire Kantian tradition by spawning highly probable theories for suppressing infinities and actually resolving these perplexities on a purely physical basis by positing curvatures of space and even of time that make them reëntrant to themselves. Heavily documented from primary sources in physics, this paper displays time’s curvature as its slowing down near very massive bodies and even freezing in a black hole from which it can reëmerge on the far side, where a new universe can open up. I argue that space curves into a double Möbius strip until it loses one dimension in exchange for another in the twin universe. It shows how 10-dimensional GUTs and the triple Universe, time/charge/parity conservation, and strange and bottom particle families and antiparticle universes, all fit together.

scholarly journals Complexity growth in integrable and chaotic models

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Vijay Balasubramanian ◽  
Matthew DeCross ◽  
Arjun Kar ◽  
Yue Li ◽  
Onkar Parrikar
Keyword(s):  
Time Evolution ◽  
Evolution Operator ◽  
Linear Growth ◽  
Conjugate Points ◽  
Majorana Fermions ◽  
Time Evolution Operator ◽  
Free Theory ◽  
Group Manifold ◽  
Geodesic Length ◽  
Evolution Trajectory

Abstract We use the SYK family of models with N Majorana fermions to study the complexity of time evolution, formulated as the shortest geodesic length on the unitary group manifold between the identity and the time evolution operator, in free, integrable, and chaotic systems. Initially, the shortest geodesic follows the time evolution trajectory, and hence complexity grows linearly in time. We study how this linear growth is eventually truncated by the appearance and accumulation of conjugate points, which signal the presence of shorter geodesics intersecting the time evolution trajectory. By explicitly locating such “shortcuts” through analytical and numerical methods, we demonstrate that: (a) in the free theory, time evolution encounters conjugate points at a polynomial time; consequently complexity growth truncates at O($$ \sqrt{N} $$ N ), and we find an explicit operator which “fast-forwards” the free N-fermion time evolution with this complexity, (b) in a class of interacting integrable theories, the complexity is upper bounded by O(poly(N)), and (c) in chaotic theories, we argue that conjugate points do not occur until exponential times O(eN), after which it becomes possible to find infinitesimally nearby geodesics which approximate the time evolution operator. Finally, we explore the notion of eigenstate complexity in free, integrable, and chaotic models.

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.

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