Geometric Justification of the Fundamental Interaction Fields for the Classical Long-Range Forces

Based on the principle of reparametrization invariance, the general structure of physically relevant classical matter systems is illuminated within the Lagrangian framework. In a straightforward way, the matter Lagrangian contains background interaction fields, such as a 1-form field analogous to the electromagnetic vector potential and symmetric tensor for gravity. The geometric justification of the interaction field Lagrangians for the electromagnetic and gravitational interactions are emphasized. The generalization to E-dimensional extended objects (p-branes) embedded in a bulk space M is also discussed within the light of some familiar examples. The concept of fictitious accelerations due to un-proper time parametrization is introduced, and its implications are discussed. The framework naturally suggests new classical interaction fields beyond electromagnetism and gravity. The simplest model with such fields is analyzed and its relevance to dark matter and dark energy phenomena on large/cosmological scales is inferred. Unusual pathological behavior in the Newtonian limit is suggested to be a precursor of quantum effects and of inflation-like processes at microscopic scales.

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LOCAL GAUGE FIELDS BASED ON A YANG–MILLS THEORY IN LOOP SPACE

International Journal of Modern Physics A ◽

10.1142/s0217751x95000504 ◽

1995 ◽

Vol 10 (07) ◽

pp. 1019-1043 ◽

Cited By ~ 5

Author(s):

SHINICHI DEGUCHI ◽

TADAHITO NAKAJIMA

Keyword(s):

Minkowski Space ◽

Loop Space ◽

Symmetric Tensor ◽

Gauge Fields ◽

Tensor Fields ◽

Yang Mills ◽

Rank Tensor ◽

Stueckelberg Formalism ◽

Mills Field ◽

Reparametrization Invariance

We construct a Yang–Mills theory in loop space (the space of all loops in Minkowski space) with the Kac–Moody gauge group in such a way that the theory possesses reparametrization invariance. On the basis of the Yang–Mills theory, we derive the usual Yang–Mills theory and a non-Abelian Stueckelberg formalism extended to local antisymmetric and symmetric tensor fields of the second rank. The local Yang–Mills field and the second-rank tensor fields are regarded as components of a Yang–Mills field on the loop space.

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Reparametrization Invariance and Some of the Key Properties of Physical Systems

Symmetry ◽

10.3390/sym13030522 ◽

2021 ◽

Vol 13 (3) ◽

pp. 522

Author(s):

Vesselin G. Gueorguiev ◽

Andre Maeder

Keyword(s):

Proper Time ◽

Hamiltonian Formulation ◽

Hamiltonian Constraint ◽

Negative Mass ◽

Principle Of Superposition ◽

Physical Systems ◽

First Order ◽

Classical Phase Space ◽

Generally Covariant ◽

Reparametrization Invariance

In this paper, we argue in favor of first-order homogeneous Lagrangians in the velocities. The relevant form of such Lagrangians is discussed and justified physically and geometrically. Such Lagrangian systems possess Reparametrization Invariance (RI) and explain the observed common Arrow of Time as related to the non-negative mass for physical particles. The extended Hamiltonian formulation, which is generally covariant and applicable to reparametrization-invariant systems, is emphasized. The connection between the explicit form of the extended Hamiltonian H and the meaning of the process parameter λ is illustrated. The corresponding extended Hamiltonian H defines the classical phase space-time of the system via the Hamiltonian constraint H=0 and guarantees that the Classical Hamiltonian H corresponds to p0—the energy of the particle when the coordinate time parametrization is chosen. The Schrödinger’s equation and the principle of superposition of quantum states emerge naturally. A connection is demonstrated between the positivity of the energy E=cp0>0 and the normalizability of the wave function by using the extended Hamiltonian that is relevant for the proper-time parametrization.

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Once the student is in control of the texts, then the texts can be manipulated, alternative arguments can be constructed and student understanding of the relevant area or topic increased. Often, a student merely hands in a precis of a string of articles, texts and cases and calls it an essay. This is not an essay presenting a serious argument for consideration, supported by evidence and it will not attract a good mark. However, the precis, or summaries, if they are well prepared, can provide the basis of argument construction and good written work. In an exam situation, as well as in coursework, students often take a lot of time discussing the facts and the outcomes of cases or the description of argument in texts, but often demonstrating little appreciation of the issues raised by the cases and little understanding of their relevance or application to the question. This is not because they are not capable of understanding but because they did not spend the proper time thinking about what the question was asking, preparing the texts to be used and constructing argument in written form. 8.2 LEARNING OUTCOMES By the end of this chapter, readers should: • be aware of the differences in approach that need to be adopted for essays and problem questions; • have confidence preparing for both types of assessment; • be able to structure work effectively; • be able to bring together the skills of reading and argument construction and demonstrate competency in writing. 8.3 PREPARATION AND STRUCTURING OF ESSAYS In answering a law essay question students are required to produced a piece of work offering a sustained argument concerning a particular question. Generally speaking, essay questions are set in the following formats: (a) A question is set to be answered. (b) A quotation is given with the bland request to discuss. (c) A quotation is given and there is a request to extract issues. Generally, an essay involves discussion in the formal sense of laying out an argument. In fact, the Latin stem of discuss is ‘discutere’ which means to ‘to dash to pieces’, a rather forceful way of describing argument. The more usual way of describing the meaning of the word ‘discuss’ is ‘to investigate or examine by argument, to sift, and to debate’. The word is often wrongly used and understood to mean just idly talking. Reading many student essays does lead one to suspect that students are idly and haphazardly just writing and wasting their hard work. Each type of essay question requires a different approach, but the same general structure is required and the same store of information can be used. This also holds true in relation to problem questions, which are discussed at the end of this chapter.

Legal Method and Reasoning ◽

10.4324/9781843145103-206 ◽

2012 ◽

pp. 265-265

Keyword(s):

Learning Outcomes ◽

Proper Time ◽

General Structure ◽

Student Understanding ◽

Hard Work ◽

Written Form ◽

Essay Question

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Clinical Update: Assessing Maximum Medical Improvement in Carpal Tunnel Syndrome

Guides Newsletter ◽

10.1001/amaguidesnewsletters.2003.julaug02 ◽

2003 ◽

Vol 8 (4) ◽

pp. 4-5

Author(s):

Christopher R. Brigham ◽

James B. Talmage

Keyword(s):

Carpal Tunnel Syndrome ◽

Carpal Tunnel ◽

Proper Time ◽

Carpal Tunnel Release ◽

Hand Function ◽

Factors Affecting ◽

Early Results ◽

Medical Evaluation ◽

Nerve Recovery ◽

Tunnel Syndrome

Abstract Permanent impairment cannot be assessed until the patient is at maximum medical improvement (MMI), but the proper time to test following carpal tunnel release often is not clear. The AMA Guides to the Evaluation of Permanent Impairment (AMA Guides) states: “Factors affecting nerve recovery in compression lesions include nerve fiber pathology, level of injury, duration of injury, and status of end organs,” but age is not prognostic. The AMA Guides clarifies: “High axonotmesis lesions may take 1 to 2 years for maximum recovery, whereas even lesions at the wrist may take 6 to 9 months for maximal recovery of nerve function.” The authors review 3 studies that followed patients’ long-term recovery of hand function after open carpal tunnel release surgery and found that estimates of MMI ranged from 25 weeks to 24 months (for “significant improvement”) to 18 to 24 months. The authors suggest that if the early results of surgery suggest a patient's improvement in the activities of daily living (ADL) and an examination shows few or no symptoms, the result can be assessed early. If major symptoms and ADL problems persist, the examiner should wait at least 6 to 12 months, until symptoms appear to stop improving. A patient with carpal tunnel syndrome who declines a release can be rated for impairment, and, as appropriate, the physician may wish to make a written note of this in the medical evaluation report.

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Expansion of the visual form field by perimeter training

PsycEXTRA Dataset ◽

10.1037/e475492008-001 ◽

1955 ◽

Cited By ~ 1

Author(s):

C. W. Crannell ◽

J. M. Christensen

Keyword(s):

Visual Form ◽

Form Field

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Cloning of the Rat Tissue Factor cDNA and Promoter: Identification of a Serum-response Region

Thrombosis and Haemostasis ◽

10.1055/s-0038-1650646 ◽

1996 ◽

Vol 76 (05) ◽

pp. 697-702 ◽

Cited By ~ 10

Author(s):

Olivier Taby ◽

Claire-Lise Rosenfield ◽

Vladimir Bogdanov ◽

Yale Nemerson ◽

Mark B Taubman

Keyword(s):

Tissue Factor ◽

General Structure ◽

Amino Acid Sequences ◽

Proximal Promoter ◽

Striking Similarity ◽

Upstream Sequence ◽

Tf Gene ◽

Rat Tissue ◽

High Degree ◽

Transcriptional Elements

SummaryTissue factor (TF) initiates coagulation and its expression in vascular smooth muscle cells (VSMC) likely plays a role in the propagation of arterial thrombosis. We report cloning the cDNA and proximal promoter region of the rat TF gene. While maintaining the general structure and organization of the TF molecule, there is a surprising divergence (≈ 18%) between the derived amino acid sequences of the rat and mouse TF. In contrast, there is striking similarity (90%) in the 5’ untranslated regions. High levels of basal promoter activity were seen in rat VSMC with constructs containing 106 bp of sequence downstream from the putative transcription start site and 426 to 103 bp of upstream sequence. Deletion of the sequence from −103 to −79, containing a single SP1 site, removed virtually all of the basal and serum-induced activity. Removal of the NFkB site or two additional upstream SP1 sites had little effect on serum responsiveness. Removal of the 5’ untranslated region abolished most of the basal activity of the TF promoter, suggesting that its high degree of conservation may be due to the presence of transcriptional elements critical for TF expression in rodent VSMC.

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