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Almost 100 years ago, two different expressions were proposed for the energy-momentum tensor of an electromagnetic wave in a dielectric. Minkowski’s tensor predicted an increase in the linear momentum of the wave on entering a dielectric medium, whereas Abraham’s tensor predicted its decrease. Theoretical arguments were advanced in favor of both sides, and… (More)

Almost a hundred years ago, two different expressions were proposed for the energy–momentum tensor of an electromagnetic wave in a dielectric. Minkowski’s tensor predicted an increase in the linear momentum of the wave on entering a dielectric medium, whereas Abraham’s tensor predicted its decrease. Theoretical arguments were advanced in favour of both… (More)

- Robert N C Pfeifer, Jutho Haegeman, Frank Verstraete
- Physical review. E, Statistical, nonlinear, and…
- 2014

The efficient evaluation of tensor expressions involving sums over multiple indices is of significant importance to many fields of research, including quantum many-body physics, loop quantum gravity, and quantum chemistry. The computational cost of evaluating an expression may depend strongly on the order in which the index sums are evaluated, and… (More)

There exist two popular energy-momentum tensors for an electromagnetic wave in a dielectric medium. The Abraham expression is robust to experimental verification but more mathematically demanding, while the Minkowski expression is the foundation of a number of simplifications commonly found within the literature, including the relative refractive index… (More)

We present several results relating to the contraction of generic tensor networks and discuss their application to the simulation of quantum many-body systems using variational approaches based upon tensor network states. Given a closed tensor network T , we prove that if the environment of a single tensor from the network can be evaluated with… (More)

For some physics students, the concept of a particle travelling faster than the speed of light holds endless fascination, and Čerenkov radiation is a visible consequence of a charged particle travelling through a medium at locally superluminal velocities. The Heaviside–Feynman equations for calculating the magnetic and electric fields of a moving charge… (More)

For some physics students, the concept of a particle travelling faster than the speed of light holds endless fascination, and Čerenkov radiation is a visible consequence of a charged particle travelling through a medium at locally superluminal velocities. The Heaviside–Feynman equations for calculating the magnetic and electric fields of a moving charge… (More)

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