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Diagrams with loops (in graph theory, these kinds of loops are called cycles, while the word loop is an edge connecting a vertex with itself) correspond to the quantum corrections to the classical field theory. Because one-loop diagrams only contain one cycle, they express the next-to-classical contributions called the semiclassical contributions.
A graph with a loop on vertex 1. In graph theory, a loop (also called a self-loop or a buckle) is an edge that connects a vertex to itself. A simple graph contains no loops. Depending on the context, a graph or a multigraph may be defined so as to either allow or disallow the presence of loops (often in concert with allowing or disallowing ...
Line chart showing the population of the town of Pushkin, Saint Petersburg from 1800 to 2010, measured at various intervals. A line chart or line graph, also known as curve chart, [1] is a type of chart that displays information as a series of data points called 'markers' connected by straight line segments. [2]
The loop is: reinforcing if, after going around the loop, one ends up with the same result as the initial assumption. balancing if the result contradicts the initial assumption. Or to put it in other words: reinforcing loops have an even number of negative links (zero also is even, see example below) balancing loops have an odd number of ...
Every graph is the line graph of some hypergraph, but, given a fixed edge size k, not every graph is a line graph of some k-uniform hypergraph. A main problem is to characterize those that are, for each k ≥ 3. A hypergraph is linear if each pair of hyperedges intersects in at most one vertex. Every graph is the line graph, not only of some ...
The stopping time T may be fixed, i.e. one may perform n steps and then loop-erase. However, it is usually more natural to take T to be the hitting time in some set. For example, let G be the graph Z 2 and let R be a random walk starting from the point (0,0).
For many massless theories, these graphs vanish in dimensional regularization (by dimensional analysis and the absence of any inherent mass scale in the loop integral). Tadpole corrections are needed if the corresponding external field has a non-zero vacuum expectation value, such as the Higgs field. [1] Tadpole diagrams were first used in the ...
Pearls in Graph Theory: A Comprehensive Introduction is an undergraduate-level textbook on graph theory by Nora Hartsfield and Gerhard Ringel.It was published in 1990 by Academic Press [1] [2] [3] with a revised edition in 1994 [4] and a paperback reprint of the revised edition by Dover Books in 2003. [5]