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  2. Minkowski distance - Wikipedia

    en.wikipedia.org/wiki/Minkowski_distance

    The Minkowski distance or Minkowski metric is a metric in a normed vector space which can be considered as a generalization of both the Euclidean distance and the Manhattan distance. It is named after the Polish mathematician Hermann Minkowski .

  3. Dirac algebra - Wikipedia

    en.wikipedia.org/wiki/Dirac_algebra

    The numbers are the components of the Minkowski metric. For this article we fix the signature to be mostly minus , that is, ( + , − , − , − ) {\displaystyle (+,-,-,-)} . The Dirac algebra is then the linear span of the identity, the gamma matrices γ μ {\displaystyle \gamma ^{\mu }} as well as any linearly independent products of the ...

  4. Gamma matrices - Wikipedia

    en.wikipedia.org/wiki/Gamma_matrices

    Then we use cyclic identity to get the two gamma-5s together, and hence they square to identity, leaving us with the trace equalling minus itself, i.e. 0. Proof of 3 If an odd number of gamma matrices appear in a trace followed by γ 5 {\displaystyle \gamma ^{5}} , our goal is to move γ 5 {\displaystyle \gamma ^{5}} from the right side to the ...

  5. Minkowski space - Wikipedia

    en.wikipedia.org/wiki/Minkowski_space

    Hermann Minkowski (1864–1909) found that the theory of special relativity could be best understood as a four-dimensional space, since known as the Minkowski spacetime.. In physics, Minkowski space (or Minkowski spacetime) (/ m ɪ ŋ ˈ k ɔː f s k i,-ˈ k ɒ f-/ [1]) is the main mathematical description of spacetime in the absence of gravitation.

  6. Lorentz group - Wikipedia

    en.wikipedia.org/wiki/Lorentz_group

    The (identity component of the) Euclidean group SE(2) is the stabilizer of a null vector, so the homogeneous space SO + (1, 3) / SE(2) is the momentum space of a massless particle; geometrically, this Kleinian geometry represents the degenerate geometry of the light cone in Minkowski spacetime.

  7. Mathematical descriptions of the electromagnetic field

    en.wikipedia.org/wiki/Mathematical_descriptions...

    Here d denotes the exterior derivative – a natural coordinate- and metric-independent differential operator acting on forms, and the (dual) Hodge star operator is a linear transformation from the space of 2-forms to the space of (4 − 2)-forms defined by the metric in Minkowski space (in four dimensions even by any metric conformal to this ...

  8. Raising and lowering indices - Wikipedia

    en.wikipedia.org/wiki/Raising_and_lowering_indices

    , is Minkowski space (or rather, Minkowski space in a choice of orthonormal basis), a model for spacetime with weak curvature. It is common convention to use greek indices when writing expressions involving tensors in Minkowski space, while Latin indices are reserved for Euclidean space.

  9. Poincaré group - Wikipedia

    en.wikipedia.org/wiki/Poincaré_group

    The Poincaré group, named after Henri Poincaré (1905), [1] was first defined by Hermann Minkowski (1908) as the isometry group of Minkowski spacetime. [2] [3] It is a ten-dimensional non-abelian Lie group that is of importance as a model in our understanding of the most basic fundamentals of physics.

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