Pure gauges 0-vacuum

M. W. Evans, P. K. Anastasovski, T. E. Bearden, et al., Energy inherent in the pure gauge vacuum, Physica Scripta (in press). 

The simplest example of the generation of energy from a pure gauge vacuum is to consider the case of an electromagnetic potential plane wave defined by... 

In a U(l) invariant theory, the pure gauge vacuum is defined by a scalar internal gauge space in which there exist the independent complex scalar fields ... 

It can be shown as follows that the transition from a pure vacuum to a pure gauge vacuum is described by the spacetime translation generator of the Poincare group. The pure vacuum on the U(l) invariant level is described by the held equations ... 

Essentially, this replacement means that the spacetime changes from one that is conformally flat to one that is conformally curved in other words, the axes vary from point to point whenever a covariant derivative is used for any gauge group symmetry. It is this variation of the axes that introduces energy into a pure gauge vacuum. The covariant derivative in the latter is... 

The action is therefore not invariant under local gauge transformation. To restore invariance the four potential, A must be introduced into the pure gauge vacuum to give the Lagrangian... 

The total Lagrangian if I X I if2 is now invariant under the local gauge transformation because of the introduction of the 4-potential A, which couples to the current of the complex A of the pure gauge vacuum. The field A also contributes to the Lagrangian, and since if + ifj + if2 is invariant, an extra term if3 appears, which must also be gauge-invariant. This can be so only if the electromagnetic field is introduced... 

Therefore, a check for self-consistency has been carried out for indices p 2 and v = 1. It has been shown, therefore, that in pure gauge theory applied to electrodynamics without a Higgs mechanism, a richly structured vacuum charge current density emerges that serves as the source of energy latent in the vacuum through the following equation ... 

The above is a pure gauge field theory. The Higgs mechanism on the U(l) level provides further sources of vacuum energy as discussed already. On the 0(3) level, the Higgs mechanism can also be applied, resulting in yet more sources of energy. 

Two 4 1 cylindrical glass(QVF) vessels with stainless steel end plates, serve as reservoirs(Figure 1) for surfactant solution(B) and water(9). Facility is available to evacuate these vessels as required by means of a rotary vacuum pump with glass cold trap in line to minimise water vapour. Another pipeline permits supply of pure nitrogen, or other gas, at low pressure, to the vessels, to provide a blanket, as desired. Proper operation and safety from over pressure is ensured by a pressure relief valve(10 in Figure 1) and the pressure gauge(P in Figure 1). 

Figure 4.4.5. DifFerential vapor-pressure apparatus. 100 ml Pyrex flasks connected (a) to a differential pressure transducer (c) with digital readout (d) and (b) to vacuum pump (e) and absolute pressure vacuum thermocouple gauge (f). The constant temperature in the water bath is maintained by a temperature controller (g). The transducer and cormecting glassware are housed in an insulated box (i) and kept at constant temperature shghtly above the measuring temperature by controller (j). Polymer solution and pure solvent (here water) are stirred by underwater magnetic stirrers (h). [Reprinted with permission from Ref. 66, Copyright 1989, American Chemical Society].

In the experiment, the back pressure of H2 (or HD, D2) gas source is 2 atm. The speed of 99.999 % pure H2, HD, and D2 (HSG) after supersonic expansion is about 1.38, 1.24, and 1.03 km/s, respectively. The H atoms are generated by vacuum gauge ionization from H2 and then blown by the molecular beam into the scattering chamber. The molecular beam speed is determined using the Rydberg tagging time-of-flight technique. 

The apparatus used to determine the pure component isotherms is illustrated in Fig. 1. This system consists simply of the adsorption cell, a constant temperature bath, a source of adsorbate (i.e., CH4), and a high-vacuum oil manometer to measure the adsorption pressure, TTie reference pressure of the manometer is monitored with a thermocouple vacuum gauge. Adsorption temperatures of 76 and 88.5 K were obtained with atmospheric baths of liquid N2 and respectively the other temperatures as measured with a copper-con-... 

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