One loop integrals reduction

Sun, Yi; Chang, Hao-Ran

doi:10.1088/1674-1137/36/11/004

Cited by 7 publications

(4 citation statements)

References 13 publications

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“…Similarly, Fong advised Jing not to be afraid of being scolded so that she could learn to reflect on and correct her mistake. This self-reflection on wrongdoings is in line with the Confucianist notion of self-cultivation that aims to achieve benevolence, righteousness, and propriety with the courage and willingness to admit to one’s misdeeds (see Sun, 2012). The teaching of self-blame and self-reflection on one’s mistakes is relevant to mental health care for individuals subscribing to the relational ethics of Confucian philosophy.…”

Section: Discussionsupporting

confidence: 52%

Journeying Through Different Mythic Worlds

Lee

2023

International Perspectives in Psychology

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The global mental health movement (GMHM) seeks to close the treatment gap in low- and middle-income countries including those in Southeast Asia. However, the GMHM has been criticized for its overemphasis on a Eurocentric approach to mental health care, ignoring the diversity of knowledge and resources in local communities. Given the pluralistic health care systems in most Southeast Asian countries, people may utilize both Indigenous healing and Western mental health services. Therefore, indigenous healing systems can be integrated into mental health care to offer additional resources to local people to cope with emotional distress. Using a single case study approach, this article aims to explore the therapeutic aspects of indigenous healing systems relevant to mental health care. The case is about Jing, a Chinese woman who simultaneously consulted psychiatrists, a dang-ki (Chinese shaman/spirit medium), and a traditional Chinese medicine physician in Singapore. I attempt to answer three questions. First, what is Jing’s experience of seeking help from different forms of healing systems? Second, what are the therapeutic aspects of indigenous healing systems relevant to mental health care? Third, what are the challenges for reconciling the experiential truth with the empirical truth? Based on her narrative, although these healing systems were structured in different mythic worlds and explanatory models, Jing found all of them helpful without experiencing any cognitive dissonance. This may be because she did not passively respond to the treatments but actively negotiated her expectations with the healers, constructed meanings, and adopted a pragmatic attitude to meet her needs.

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Section: Discussionsupporting

confidence: 52%

Journeying Through Different Mythic Worlds

Lee

2023

International Perspectives in Psychology

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“…In addition, other authors have been made investigations by using the procedure adopted in the present work. In particular in [31] the authors explored some very interesting aspects of the systematization proposed in [2] concluding that there are important advantages relative to the traditional ones.…”

Section: Ambiguities and Symmetry Relationsmentioning

confidence: 99%

A Systematization for One-Loop 4D Feynman Integrals-Different Species of Massive Fields

Battistel¹,

Dallabona²

2012

JMP

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A systematization for the manipulations and calculations involving divergent (or not) Feynman integrals, typical of the one loop perturbative solutions of Quantum Field Theory, is proposed. A previous work on the same issue is generalized to treat theories and models having different species of massive fields. An improvement on the strategy is adopted so that no regularization needs to be used. The final results produced, however, can be converted into the ones of reasonable regularizations, especially those belonging to the dimensional regularization (in situations where the method applies). Through an adequate interpretation of the Feynman rules and a convenient representation for involved propagators, the finite and divergent parts are separated before the introduction of the integration in the loop momentum. Only the finite integrals obtained are in fact integrated. The divergent content of the amplitudes are written as a combination of standard mathematical object which are never really integrated. Only very general scale properties of such objects are used. The finite parts, on the other hand, are written in terms of basic functions conveniently introduced. The scale properties of such functions relate them to a well defined way to the basic divergent objects providing simple and transparent connection between both parts in the assintotic regime. All the arbitrariness involved in this type of calculations are preserved in the intermediary steps allowing the identification of universal properties for the divergent integrals, which are required for the maintenance of fundamental symmetries like translational invariance and scale independence in the perturbative amplitudes. Once these consistency relations are imposed no other symmetry is violated in perturbative calculations neither ambiguous terms survive at any theory or model formulated at any space-time dimension including nonrenormalizable cases. Representative examples of perturbative amplitudes involving different species of massive fermions are considered as examples. The referred amplitudes are calculated in detail within the context of the presented strategy (and systematization) and their relations among other Green functions are explicitly verified. At the end a generalization for the finite functions is presented

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“…With the help of PVRS, a huge number of OLFDs can be automatically assembled from a small number of basic building blocks [6,8,9]. Owing to this advantage, the PVRS triggered many variants [9][10][11][12][13][14][15][16][17][18][19][20] and program packages [20][21][22][23][24][25] for automatic algebraic calculation, and has been widely applied in numerous processes of high energy physics.…”

mentioning

confidence: 99%

“…PVRS [6] and its variants [8][9][10][11][12][13][14][15][16][17][18][19][20] are well established for particle physics which is the Lorentz-invariant system, however, there have been only sparse attempts [26][27][28] to generalize the PVRS from particle physics to other subfields in which the Lorentz invariance is absent, such as nuclear physics and condensed matter physics. On the other hand, the OLFDs in these two subfields are more complicated than that in particle physics due to finite temperature, finite density (chemical potential), or pseudo-relativistic dispersion.…”

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confidence: 99%

Generalized Passarino-Veltman reduction scheme in the absence of Lorentz invariance

Chang¹

2020

Preprint

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Passarino-Veltman reduction scheme (PVRS) offers an efficient procedure to reduce the one-loop Feynman diagrams (OLFDs). It is well established and widely applied in the system of particle physics where the Lorentz invariance is present, but there have been only sparse attempts to generalize it to other subfields in which the Lorentz invariance is lacking, such as nuclear physics and condensed matter physics. We report a systematic theoretical framework by presenting two equivalent generalized PVRS (GPVRS) in the absence of Lorentz invariance. We apply the GPVRS to simplify several typical OLFDs in different important models of relativistic particles or pseudorelativistic quasi-particles at finite temperature and/or finite density. We verify our results by gauge invariance and various limiting cases. The GPVRS can analyze the OLFDs in a wide range of physical systems without Lorentz invariance, such as quark-gluon plasma in nuclear physics and Dirac topological materials in condensed matter physics.

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One loop integrals reduction

Abstract: By further examining the symmetry of external momenta and masses in Feynman integrals, we fulfilled the method proposed by Battistel and Dallabona, and showed that recursion relations in this method can be applied to simplify Feynman integrals directly.

Cited by 7 publications

References 13 publications

Journeying Through Different Mythic Worlds

Journeying Through Different Mythic Worlds

A Systematization for One-Loop 4D Feynman Integrals-Different Species of Massive Fields

Generalized Passarino-Veltman reduction scheme in the absence of Lorentz invariance

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