An Introduction to Tensors and Group Theory for PhysicistsAn Introduction to Tensors and Group Theory for Physicists provides both an intuitive and rigorous approach to tensors and groups and their role in theoretical physics and applied mathematics. A particular aim is to demystify tensors and provide a unified framework for understanding them in the context of classical and quantum physics. Connecting the component formalism prevalent in physics calculations with the abstract but more conceptual formulation found in many mathematical texts, the work will be a welcome addition to the literature on tensors and group theory. Advanced undergraduate and graduate students in physics and applied mathematics will find clarity and insight into the subject in this textbook. |
Contents
Linear Algebra and Tensors | 2 |
Group Theory | 84 |
Complexifications of Real Lie Algebras and the Tensor Product Decomposition of sl2CR Representations | 227 |
| 234 | |
| 235 | |
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An Introduction to Tensors and Group Theory for Physicists Nadir Jeevanjee No preview available - 2016 |
Common terms and phrases
adjoint representation angular momentum antisymmetric tensor arbitrary basis vectors bilinear bracket commutation relations complex vector space complex-linear components consider corresponding decompose decomposition defined definition denoted dimension Dirac spinor direct sum discussion dual vectors eigenvalues eigenvectors elements equation equivalent Example Exercise fact finite-dimensional function fundamental representation given GL(n GL(V group G hence highest weight vector Hilbert space identity induced Lie algebra inner product interpreted intertwiner invariant subspace inverse irreducible representations irreps Isom(V isometry isomorphism Lie algebra representation linear operator matrix Lie group notation Note one-to-one orthogonal orthonormal basis particle physics polynomial Problem Proposition prove pseudovector quantum mechanics real vector space representation of G representation of su(2 rigid body rotation satisfies SO(n span spin standard basis subgroup symmetric tensor tensor product tensor product representation tion unitary usual vector space verify