Inhomogeneous Transformation

The transformations = F( ) will be called internal isometric transformations. They transform any NC to a NC with the same set of distances. In many cases they may be expressed as linear inhomogeneous transformations... 

Next we consider the direct sum of the two transformation groups j/ JO and SS In the case where both these groups may be represented by linear inhomogeneous transformations according to Eqs. (2.6), (2.28) this leads to the matrix group... 

The set of all inhomogeneous Lorentz transformations form a ten-parameter group, usually called the Poincar6 group. 

Note that the scalar product is formally the same as in the nonrela-tivistic case it is, however, now required to be invariant under all orthochronous inhomogeneous Lorentz transformations. The requirement of invariance under orthochronous inhomogeneous Lorentz transformations stems of course from the homogeneity and isotropy of space-time, send corresponds to the assertion that all origins and orientation of the four-dimensional space time manifold are fully equivalent for the description of physical phenomena. 

Consider next the relativistic invariance of quantum electrodynamics. Again, loosely speaking, we say that quantum electrodynamics is relativistically invariant if its observable consequences are the same in all frames connected by an inhomogeneous Lorentz transformation a,A ... 

We have noted that the unitary operators U(a,A) define a representation of the inhomogeneous group. If we denote by P and AT, the (hermitian) generators for infinitesimal translations and Lorentz transformations respectively, then... 

Similar considerations lead to the transformation properties of the one-photon states and of the photon in -operators which create photons of definite momentum and helicity. We shall, however, omit them here. Suffice it to remark that the above transformation properties imply that the interaction hamiltonian density Jf mAz) = transforms like a scalar under restricted inhomogeneous Lorentz transformation... 

The invariance of the theory under inhomogeneous Lorentz transformation implies that a unitary U(a,A) exists, such that... 

Lorentz invariant scalar product, 499 of two vectors, 489 Lorentz transformation homogeneous, 489,532 improper, 490 inhomogeneous, 491 transformation of matrix elements, 671... 

Quantization of radiation field in terms of field intensity operators, 562 Quantum electrodynamics, 642 asymptotic condition, 698 gauge invariance in relation to operators inducing inhomogeneous Lorentz transformations, 678 invariance properties, 664 invariance under discrete transformations, 679... 

Under the shift (42) to the TS trajectory as a moving origin, the leading term Ho takes the form of Eq. (55). The higher terms transform into inhomogeneous polynomials... 

In the context of the Rabkin and Skripnyuk model, which requires that desorption is better approximation of equilibrium then absorption, the high value of the enthalpy of desorption observed for a reactively synthesized MgH in Fig. 2.43b seems to be correct. If so, the hysteresis in Fig. 2.43a is due to higher enthalpy of desorption rather than to an inhomogeneity in the fraction transformed and non-transformed particles during the absorption process. 

---