Wolfgang Ludwig – författare

Includes a revised taxonomic outline for the phyla Bacteroidetes, Planctomycetes, Chlamydiae, Spirochetes, Fibrobacteres, Fusobacteria, Acidobacteria, Verrucomicrobia, Dictyoglomi, and Gemmatimonadetes based upon the SILVA project as well as a description of more than 153 genera in 29 families. Includes many medically important taxa.

Includes a revised taxonomic outline for the Firmicutes based upon the SILVA project as well as a description of more than 1346 species and 235 genera belonging to the phylum Firmicutes, which are also called the low mol% G+C Gram positive prokaryotes. Major taxa to be included are Alicyclobacillus, Bacillus, Clostridium, Enterococcus, Erysipelothrix, Eubacterium, Haloanaerobium, Heliobacterium, Lachnospira, Lactobacillus, Leuconostoc, Listeria, Paenibacillus, Peptococcus, Ruminococcus, Staphylococcus, Streptococcus, Syntrophomonas, Thermoactinomyces, Thermoanaerobacter, Veillonella and 229 additional genera. Includes many medically and industrially important taxa.

Includes a revised taxonomic outline for the phyla Bacteroidetes, Planctomycetes, Chlamydiae, Spirochetes, Fibrobacteres, Fusobacteria, Acidobacteria, Verrucomicrobia, Dictyoglomi, and Gemmatimonadetes based upon the SILVA project as well as a description of more than 153 genera in 29 families. Includes many medically important taxa.

Includes a revised taxonomic outline for the Actinobacteria or the high G+C Gram positives is based upon the SILVA project as well as a description of greater than 200 genera in 49 families. Includes many medically and industrially important taxa.

Includes a revised taxonomic outline for the phyla Bacteroidetes, Planctomycetes, Chlamydiae, Spirochetes, Fibrobacteres, Fusobacteria, Acidobacteria, Verrucomicrobia, Dictyoglomi, and Gemmatimonadetes based upon the SILVA project as well as a description of more than 153 genera in 29 families. Includes many medically important taxa.

Includes a revised taxonomic outline for the Actinobacteria or the high G+C Gram positives is based upon the SILVA project as well as a description of greater than 200 genera in 49 families. Includes many medically and industrially important taxa.

heit aufgeiaßt werden muß. Dabei werden sich als Resultate von zentraler Be­ deutung ergeben: Diejenige Größe, welche die ganze Thermodynamik beherrscht, nämlich die Entropie, erweist sich als quantitatives Maß der soeben geschilderten Unkenntnis. Das ist fraglos eine der merkwürdigsten und tiefstliegenden Aus­ sagen der ganzen Physik. Sie wird natürlich nur sinnvoll durch eine exakte Formulierung, welche erst nach den Vorarbeiten der nächsten Abschnitte erfolgen kann. Ein beherrschender Zug der statistischen Mechanik besteht darin, daß die Zahl der mikroskopischen Freiheitsgrade - im wesentlichen gegeben durch die Zahl N der im System enthaltenen Atome - so ungeheuer groß ist. Obwohl mit wachsendem N unsere Kenntnis von der mikroskopischen Struktur immer geringer wird, werden dennoch die oben angedeuteten Wahrscheinlichkeitsaus­ sagen über makroskopische Größen um so schärfer, je größer N ist, in dem Sinne, daß wir im Limes N -+ oo wieder zu sicheren Aussagen gelangen. Dieser Zug der Wahrscheinlichkeitsrechnung ist so charakteristisch, daß wir ihn gleich jetzt an einem primitiven Beispiel erläutern wollen. Ein Gas bestehe aus N Molekülen, welche sich unabhängig voneinander in einem Volumen V bewegen (ideales Gas). Wir grenzen innerhalb V ein dagegen kleines Volumen v ab und interessieren uns für die Zahl n der Moleküle, welche sich in v aufhalten. Nennen wir V und 1-p = q, -y=P so sind p bzw. q die Wahrscheinlichkeiten dafür, ein hervorgehobenes Molekül innerhalb bzw. außerhalb v zu finden.

Symmetries in Physics presents the fundamental theories of symmetry, together with many examples of applications taken from several different branches of physics. Emphasis is placed on the theory of group representations and on the powerful method of projection operators. The excercises are intended to stimulate readers to apply the techniques demonstrated in the text.

Symmetries in Physics presents the fundamental theories of symmetry, together with many examples of applications taken from several different branches of physics. Emphasis is placed on the theory of group representations and on the powerful method of projection operators. The excercises are intended to stimulate readers to apply the techniques demonstrated in the text.

Everyone knows that symmetry is fundamentally important in physics. On one hand, the symmetry of a system is often the starting point for general physical considerations, and on the other hand, particular problems may be solved in simpler and more elegant ways if symmetry is taken into account. This book presents the underlying theories of symmetry and gives examples of their application in branches of physics ranging from solid-state to high-energy physics via atomic and molecular physics. The text is as self-contained as possible, with as much mathematical formalism given as required. The main emphasis is on the theory of group representations and on the method of projection operators, this is a very powerful tool which is often treated only very briefly. Discrete symmetries, continuous symmetries and symmetry breaking are also discussed, and exercises are provided to stimulate the reader to carry out original work.