$\require{mediawiki-texvc}$

연합인증

연합인증 가입 기관의 연구자들은 소속기관의 인증정보(ID와 암호)를 이용해 다른 대학, 연구기관, 서비스 공급자의 다양한 온라인 자원과 연구 데이터를 이용할 수 있습니다.

이는 여행자가 자국에서 발행 받은 여권으로 세계 각국을 자유롭게 여행할 수 있는 것과 같습니다.

연합인증으로 이용이 가능한 서비스는 NTIS, DataON, Edison, Kafe, Webinar 등이 있습니다.

한번의 인증절차만으로 연합인증 가입 서비스에 추가 로그인 없이 이용이 가능합니다.

다만, 연합인증을 위해서는 최초 1회만 인증 절차가 필요합니다. (회원이 아닐 경우 회원 가입이 필요합니다.)

연합인증 절차는 다음과 같습니다.

최초이용시에는
ScienceON에 로그인 → 연합인증 서비스 접속 → 로그인 (본인 확인 또는 회원가입) → 서비스 이용

그 이후에는
ScienceON 로그인 → 연합인증 서비스 접속 → 서비스 이용

연합인증을 활용하시면 KISTI가 제공하는 다양한 서비스를 편리하게 이용하실 수 있습니다.

Combinatorics in tensor-integral reduction 원문보기

European journal of physics : a journal of the European Physical Society, v.38 no.2, 2017년, pp.025801 -   

Ee, June-Haak (Department of Physics, Korea University, Seoul 02841, Korea) ,  Jung, Dong-Won (Department of Physics, Korea University, Seoul 02841, Korea) ,  Kim, U-Rae (Department of Physics, Korea University, Seoul 02841, Korea) ,  Lee, Jungil (Department of Physics, Korea University, Seoul 02841, Korea)

Abstract AI-Helper 아이콘AI-Helper

We illustrate a rigorous approach to express the totally symmetric isotropic tensors of arbitrary rank in the n-dimensional Euclidean space as a linear combination of products of Kronecker deltas. By making full use of the symmetries, one can greatly reduce the efforts to compute cumbersome angular ...

참고문헌 (23)

  1. [1] Battaglia F and George T F 2013 Tensors: a guide for undergraduate students Am. J. Phys. 81 498 10.1119/1.4802811 Tensors: a guide for undergraduate students Battaglia F and George T F Am. J. Phys. 0002-9505 81 2013 498 

  2. [2] See, for exampleFeynman R P, Leighton R B and Sands M 1963 The Feynman Lectures on Physics (Reading, MA: Addison-Wesley) ch 31 Feynman R P, Leighton R B and Sands M The Feynman Lectures on Physics 1963 

  3. [3] Smith G F 1968 On isotropic tensors and rotation tensors of dimension m and order n Tensor, N.S. 19 79 On isotropic tensors and rotation tensors of dimension m and order n Smith G F Tensor, N.S. 0040-3504 19 1968 79 

  4. [4] Smith G F 1970 The crystallographic property tensors of orders 1 to 8 Ann. New York Acad. Sci. 172 59 10.1111/j.1749-6632.1970.tb34968.x The crystallographic property tensors of orders 1 to 8 Smith G F Ann. New York Acad. Sci. 0077-8923 172 1970 59 

  5. [5] Smith G F 1971 On isotropic functions of symmetric tensors, skew-symmetric tensors and vectors Int. J. Eng. Sci. 9 899 10.1016/0020-7225(71)90023-1 On isotropic functions of symmetric tensors, skew-symmetric tensors and vectors Smith G F Int. J. Eng. Sci. 0020-7225 9 1971 899 

  6. [6] Kearsley E A and Fong J T 1975 Linearly independent sets of isotropic Cartesian tensors of ranks up to eight J. Res. Natl Bur. Stand. B 79B 49 10.6028/jres.079B.005 Linearly independent sets of isotropic Cartesian tensors of ranks up to eight Kearsley E A and Fong J T J. Res. Natl Bur. Stand. 0022-4332 79B B 1975 49 

  7. [7] Hinze J O 1975 Turbulence 2nd edn (New York: McGraw-Hill) Hinze J O Turbulence 1975 

  8. [8] Robertson H P 1940 The invariant theory of isotropic turbulence Math. Proc. Camb. Phil. Soc. 36 209 10.1017/S0305004100017199 The invariant theory of isotropic turbulence Robertson H P Math. Proc. Camb. Phil. Soc. 0305-0041 36 1940 209 

  9. [9] Champagne F H 1978 The fine-scale structure of the turbulent velocity field J. Fluid Mech. 86 67 10.1017/S0022112078001019 The fine-scale structure of the turbulent velocity field Champagne F H J. Fluid Mech. 0022-1120 86 1978 67 

  10. [10] Kielich S 1961 The second virial coefficient for polar gas mixtures Acta Phys. Pol. 20 433 The second virial coefficient for polar gas mixtures Kielich S Acta Phys. Pol. 0001-673X 20 1961 433 

  11. [11] Healy W P 1975 On the isotropic averaging of fifth-order Cartesian tensors J. Phys. A: Math. Gen. 8 L87 10.1088/0305-4470/8/9/001 On the isotropic averaging of fifth-order Cartesian tensors Healy W P J. Phys. A: Math. Gen. 0305-4470 8 9 001 1975 L87 

  12. [12] Andrews D L and Thirunamachandran T 1977 On three-dimensional rotational averages J. Chem. Phys. 67 5026 10.1063/1.434725 On three-dimensional rotational averages Andrews D L and Thirunamachandran T J. Chem. Phys. 67 1977 5026 

  13. [13] Andrews D L and Ghoul W A 1981 Eighth rank isotropic tensors and rotational averages J. Phys. A: Math. Gen. 14 1281 10.1088/0305-4470/14/6/008 Eighth rank isotropic tensors and rotational averages Andrews D L and Ghoul W A J. Phys. A: Math. Gen. 0305-4470 14 6 008 1981 1281 

  14. [14] ’t Hooft G and Veltman M 1972 Regularization and renormalization of gauge fields Nucl. Phys. B 44 189 10.1016/0550-3213(72)90279-9 Regularization and renormalization of gauge fields ’t Hooft G and Veltman M Nucl. Phys. 0550-3213 44 B 1972 189 

  15. [15] Bollini C G and Giambiagi J J 1972 Dimensional renormalization: the number of dimensions as a regularizing parameter Nuovo Cimento B 12 20 10.1007/BF02895558 Dimensional renormalization: the number of dimensions as a regularizing parameter Bollini C G and Giambiagi J J Nuovo Cimento 0369-3554 12 B 1972 20 

  16. [16] Bollini C G and Giambiagi J J 1972 Lowest order ‘divergent’ graphs in &ngr;-dimensional space Phys. Lett. B 40 566 10.1016/0370-2693(72)90483-2 Lowest order ‘divergent’ graphs in &ngr;-dimensional space Bollini C G and Giambiagi J J Phys. Lett. 0370-2693 40 B 1972 566 

  17. [17] ’t Hooft G 1973 Dimensional regularization and the renormalization group Nucl. Phys. B 61 455 10.1016/0550-3213(73)90376-3 Dimensional regularization and the renormalization group ’t Hooft G Nucl. Phys. 0550-3213 61 B 1973 455 

  18. [18] ’t Hooft G 1973 An algorithm for the poles at dimension four in the dimensional regularization procedure Nucl. Phys. B 62 444 10.1016/0550-3213(73)90263-0 An algorithm for the poles at dimension four in the dimensional regularization procedure ’t Hooft G Nucl. Phys. 0550-3213 62 B 1973 444 

  19. [19] Passarino G and Veltman M 1979 One-loop corrections for e + e − annihilation into &mgr; + &mgr; − in the Weinberg model Nucl. Phys. B 160 151 10.1016/0550-3213(79)90234-7 One-loop corrections for e + e − annihilation into &mgr; + &mgr; − in the Weinberg model Passarino G and Veltman M Nucl. Phys. 0550-3213 160 B 1979 151 

  20. [20] Zelevinsky V 2011 Quantum Physics: Volume 1: From Basics to Symmetries and Perturbations (Weinheim: Wiley) ch 16 Zelevinsky V Quantum Physics: Volume 1: From Basics to Symmetries and Perturbations 2011 

  21. [21] Gram J P 1879 Om raekkeudviklinger, bestemte ved hjaelp af de mindste kvadraters methode Copenhagen Gram J P 1879 

  22. [22] Weyl H 1939 The Classical Groups (Princeton, NJ: Princeton University Press) Weyl H The Classical Groups 1939 

  23. [23] Jeffreys H 1973 On isotropic tensors Proc. Camb. Phil. Soc. 73 173 10.1017/S0305004100047587 On isotropic tensors Jeffreys H Proc. Camb. Phil. Soc. 0008-1981 73 1973 173 

LOADING...

관련 콘텐츠

오픈액세스(OA) 유형

GREEN

저자가 공개 리포지터리에 출판본, post-print, 또는 pre-print를 셀프 아카이빙 하여 자유로운 이용이 가능한 논문

이 논문과 함께 이용한 콘텐츠

저작권 관리 안내
섹션별 컨텐츠 바로가기

AI-Helper ※ AI-Helper는 오픈소스 모델을 사용합니다.

AI-Helper 아이콘
AI-Helper
안녕하세요, AI-Helper입니다. 좌측 "선택된 텍스트"에서 텍스트를 선택하여 요약, 번역, 용어설명을 실행하세요.
※ AI-Helper는 부적절한 답변을 할 수 있습니다.

선택된 텍스트

맨위로